Algebra 84

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 3, 1, 5 ] 
[ 1, 5, 3 ] - [ 1, 8, 3 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 1 0 1 1 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  120    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  273    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  275    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  276    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 106

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 8, 3, 4, 5, 2 ] 
[ 4, 5, 2, 8, 3 ] 
[ 5, 2, 8, 3, 4 ] 
[ 5, 2, 6 ] 
[ 3, 4, 5, 2, 8 ] 
[ 2, 6, 5 ] - [ 2, 8, 3, 4, 5 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(0 1 1 1 1 1 1 1)
(0 1 1 1 1 0 0 0)
(0 1 0 1 1 0 0 1)
(0 1 1 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  182    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  333    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  110    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  335    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  336    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 110

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 6 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 5, 3 ] 
[ 2, 6, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 1 1 1 0 1 1 1)
(0 1 1 1 0 1 1 1)
(0 1 1 1 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  186    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  344    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  106    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  345    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  346    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 120

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 5, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 1, 5 ] 
[ 1, 5, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(1 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 0 0 0 1)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  365    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   84    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  366    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  368    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  369    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 182

Quiver

[ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 8, 3, 4, 5, 2 ] 
[ 4, 5, 2, 8, 3 ] 
[ 5, 2, 8, 3, 4 ] 
[ 5, 2, 6 ] 
[ 3, 4, 5, 2, 8 ] 
[ 2, 6, 5 ] - [ 2, 8, 3, 4, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 1 1)
(1 1 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(1 1 1 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  106    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  492    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  186    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  494    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  495    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 186

Quiver

[ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 6 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 5, 3 ] 
[ 2, 6, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 1 1 1)
(1 1 1 1 0 0 0 0)
(1 1 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  110    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  503    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  182    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  504    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  505    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 258

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 5, 1 ] 
[ 8, 3, 4, 5, 1 ] 
[ 4, 5, 1, 8, 3 ] 
[ 5, 1, 8, 3, 4 ] 
[ 5, 1, 6 ] 
[ 3, 4, 5, 1, 8 ] 
[ 1, 6, 5 ] - [ 1, 8, 3, 4, 5 ] 

Cartan matrix

(1 0 1 1 1 1 1 1)
(1 1 1 1 1 0 0 0)
(1 0 1 1 1 0 0 0)
(1 0 0 1 1 0 0 1)
(1 0 1 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  314    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  273    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  262    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  649    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  354    permutation [ 2, 3, 5, 1, 6, 7, 8, 4 ]

Algebra 262

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 4, 1 ] 
[ 8, 3, 4, 1 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 1, 6 ] 
[ 3, 4, 1, 8 ] 
[ 4, 1, 8, 3 ] - [ 4, 5, 3 ] 
[ 1, 6, 4 ] - [ 1, 8, 3, 4 ] 

Cartan matrix

(1 0 1 1 0 1 1 1)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  318    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  287    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  258    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  655    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  656    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 273

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 8 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 5, 1 ] 
[ 8, 3, 5, 1 ] 
[ 3, 4, 2 ] 
[ 5, 1, 8, 3 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 5, 1, 6 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 1, 6, 5 ] - [ 1, 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 1, 8 ] 

Cartan matrix

(1 0 1 0 1 1 1 1)
(1 1 1 0 1 0 0 0)
(1 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(1 0 0 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 1 0 0 1)

Good mutations

vertex  2 -> Algebra  366    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  277    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra  258    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra   84    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  679    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  680    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 275

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 3, 1, 5 ] 
[ 1, 5, 3 ] - [ 1, 8, 3 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 1 0 1 1 0 1)
(1 1 1 0 0 0 0 0)
(1 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  368    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  679    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  684    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   84    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  685    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 276

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 1 ] 
[ 3, 8, 4, 2 ] 
[ 2, 3, 8, 4 ] 
[ 3, 8, 1, 5 ] 
[ 1, 5, 3, 8 ] 
[ 4, 2, 3, 8 ] 
[ 8, 1, 5, 3 ] - [ 8, 4, 2, 3 ] 

Cartan matrix

(1 0 1 0 1 1 1 0)
(1 1 1 0 0 0 0 1)
(1 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 0)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  686    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  369    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  286    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  653    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  680    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  685    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   84    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 277

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 5, 8 ], [ 6, 3 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 5, 2 ] 
[ 2, 3, 5 ] 
[ 8, 3, 5 ] 
[ 3, 1, 6 ] 
[ 1, 6, 3 ] - [ 1, 8, 3 ] 
[ 5, 2, 3 ] - [ 5, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 0 1 0 0 1 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 1 0 0 1)
(0 1 1 1 1 0 0 1)
(0 1 1 0 1 0 0 1)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  380    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  287    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  273    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra  688    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  689    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  690    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 286

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 5, 3, 1 ] 
[ 1, 5, 3 ] 
[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 2, 3, 8 ] 
[ 5, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 5, 3 ] 
[ 3, 1, 5 ] - [ 3, 8, 5 ] 

Cartan matrix

(1 0 0 0 1 1 1 0)
(1 1 1 0 0 0 0 0)
(1 1 1 1 1 1 1 1)
(0 1 0 1 0 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  704    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  307    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  705    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  703    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  276    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 287

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 6, 3 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 3, 1, 6 ] 
[ 1, 6, 3 ] - [ 1, 8, 3 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 1 0 0 1 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  401    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  262    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  277    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  707    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  708    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  709    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 307

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 5, 4, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 1, 5, 4 ] 
[ 2, 3, 4, 8 ] 
[ 5, 4, 8 ] 
[ 8, 2, 3, 4 ] - [ 8, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 8, 5 ] 

Cartan matrix

(1 0 0 0 1 1 1 0)
(1 1 1 1 0 0 0 0)
(1 0 1 1 1 1 1 1)
(1 1 0 1 1 1 1 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  737    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  286    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  735    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  653    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 314

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 5, 1 ] 
[ 8, 2, 4, 5, 1 ] 
[ 4, 5, 1, 8, 2 ] 
[ 5, 1, 8, 2, 4 ] 
[ 5, 1, 6 ] 
[ 2, 4, 5, 1, 8 ] 
[ 1, 6, 5 ] - [ 1, 8, 2, 4, 5 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 1 1 1 0 0 0)
(0 0 1 0 0 0 0 0)
(1 0 0 1 1 0 0 1)
(1 1 1 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  329    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  258    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  318    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  755    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  513    permutation [ 3, 2, 5, 1, 6, 7, 8, 4 ]

Algebra 318

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 6, 4 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 4, 1 ] 
[ 8, 2, 4, 1 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 4, 1, 6 ] 
[ 2, 4, 1, 8 ] 
[ 4, 1, 8, 2 ] - [ 4, 5, 2 ] 
[ 1, 6, 4 ] - [ 1, 8, 2, 4 ] 

Cartan matrix

(1 1 1 1 0 1 1 1)
(1 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(1 1 1 1 1 0 0 1)
(0 1 1 0 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  344    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  262    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  314    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  761    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  762    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 329

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 5, 1 ] 
[ 8, 2, 5, 1 ] 
[ 4, 8, 2 ] 
[ 5, 1, 8, 2 ] 
[ 4, 8, 3 ] 
[ 5, 1, 6 ] 
[ 3, 4, 8 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 1, 6, 5 ] - [ 1, 8, 2, 5 ] 
[ 2, 4, 8 ] - [ 2, 5, 1, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 0 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(0 0 0 1 0 0 0 1)
(1 0 1 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  783    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  333    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  366    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  314    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  7 -> Algebra  785    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  715    permutation [ 3, 5, 1, 6, 7, 8, 4, 2 ]

Algebra 333

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 2, 1 ] 
[ 8, 2, 1 ] 
[ 5, 8, 2 ] 
[ 4, 5, 8, 3 ] 
[ 5, 8, 3, 4 ] 
[ 2, 1, 6 ] 
[ 3, 4, 5, 8 ] 
[ 1, 6, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 3, 4, 5 ] 
[ 2, 1, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 1 0 1 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 0 1 1 0 0 1)
(0 0 1 0 1 0 0 1)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  792    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  106    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  370    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  344    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  329    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra  794    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  795    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 335

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 8, 3, 4, 5, 2 ] 
[ 4, 5, 2, 8, 3 ] 
[ 5, 2, 8, 3, 4 ] 
[ 5, 2, 6 ] 
[ 3, 4, 5, 2, 8 ] 
[ 2, 6, 5 ] - [ 2, 8, 3, 4, 5 ] 

Cartan matrix

(1 1 1 1 1 1 0 1)
(0 1 1 1 1 1 0 1)
(0 1 1 1 1 0 0 0)
(0 1 0 1 1 0 0 1)
(0 1 1 0 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  494    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  794    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  346    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  106    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  800    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 336

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 5, 2 ] 
[ 4, 5, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 2, 3, 4 ] 
[ 5, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 4, 5, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(0 1 1 1 1 1 1 0)
(0 1 1 1 1 0 0 1)
(0 1 0 1 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  495    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  801    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  800    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  106    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 344

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 2, 1 ] 
[ 8, 2, 1 ] 
[ 4, 8, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 1, 6 ] 
[ 3, 4, 8 ] 
[ 1, 6, 2 ] - [ 1, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 1, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 1 1 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  816    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  110    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  401    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  318    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra  333    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  817    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  818    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 345

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 8, 3, 4, 6, 2 ] 
[ 5, 3, 4 ] 
[ 6, 2, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 6, 2, 7 ] 
[ 3, 4, 6, 2, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 2, 8, 3 ] 
[ 2, 7, 6 ] - [ 2, 8, 3, 4, 6 ] 

Cartan matrix

(1 1 1 1 0 1 1 1)
(0 1 1 1 0 1 1 1)
(0 1 1 1 0 1 0 0)
(0 1 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(0 1 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra  504    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  820    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  348    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  6 -> Algebra  110    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 346

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 6 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 5, 3 ] 
[ 2, 6, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 1 1 1 0 1 0 1)
(0 1 1 1 0 1 0 1)
(0 1 1 1 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 0 0 1 1 1 0 0)
(0 0 0 1 1 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  505    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  818    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  335    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  110    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 348

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 4 ], [ 8, 3 ]

Relations

[ 7, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 4, 2, 7 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 6, 3 ] 
[ 2, 7, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 1 1 1 0 0 1 1)
(0 1 1 1 0 0 1 1)
(0 1 1 1 0 0 0 0)
(0 1 1 1 0 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 0 0 1 0 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  507    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  827    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  354    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  345    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra  649    permutation [ 4, 1, 2, 8, 3, 6, 5, 7 ]

Algebra 354

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 7, 4 ], [ 8, 3 ]

Relations

[ 7, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 7 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 5, 3 ] 
[ 2, 7, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 1 1 1 0 0 1 1)
(0 1 1 1 0 0 1 1)
(0 1 1 1 0 0 0 0)
(0 1 1 1 1 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 1 1 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  513    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  837    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  348    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  258    permutation [ 4, 1, 2, 8, 3, 5, 6, 7 ]

Algebra 365

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 2, 3, 4, 8, 1 ] 
[ 3, 4, 8, 1, 2 ] 
[ 4, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 4 ] 
[ 1, 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 0 0 0 1)
(1 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  120    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  852    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  854    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 366

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 5, 1 ] 
[ 8, 2, 5, 1 ] 
[ 3, 4, 8, 2 ] 
[ 5, 1, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 5, 1, 6 ] 
[ 1, 6, 5 ] - [ 1, 8, 2, 5 ] 
[ 2, 3, 4, 8 ] - [ 2, 5, 1, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 1 0 0 1)
(1 0 0 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  856    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  370    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  273    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  329    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  120    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  858    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  859    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 368

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 5, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 1, 5 ] 
[ 1, 5, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 1 1 0 1)
(1 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 0 0 0 1)
(0 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  854    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  275    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  858    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  863    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  120    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  864    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 369

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 5, 2, 8, 1 ] 
[ 3, 4, 2 ] 
[ 4, 2, 3 ] 
[ 2, 8, 1, 5 ] 
[ 1, 5, 2, 8 ] 
[ 4, 2, 8 ] 
[ 8, 1, 5, 2 ] - [ 8, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 

Cartan matrix

(1 1 1 0 1 1 1 0)
(1 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 0 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  3 -> Algebra  276    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  791    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  859    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  864    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  120    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 370

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 2, 1 ] 
[ 8, 2, 1 ] 
[ 5, 8, 2 ] 
[ 4, 8, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 4 ] 
[ 2, 1, 6 ] 
[ 1, 6, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 3, 5 ] 
[ 2, 1, 8 ] - [ 2, 5, 8 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(1 1 0 0 1 0 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 0 0 0 1)
(0 0 0 0 1 0 0 1)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  866    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  380    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra  333    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  366    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra  868    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  869    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 371

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 8, 3, 5, 6, 2 ] 
[ 4, 8, 3 ] 
[ 5, 6, 2, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 2, 8, 3, 5 ] 
[ 6, 2, 7 ] 
[ 2, 7, 6 ] - [ 2, 8, 3, 5, 6 ] 
[ 3, 4, 8 ] - [ 3, 5, 6, 2, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(0 1 1 0 1 1 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 1)
(0 1 0 0 1 1 0 1)
(0 1 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  528    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  872    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 380

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 5, 8, 2 ] 
[ 5, 8, 2, 3 ] 
[ 8, 2, 3, 5 ] 
[ 2, 1, 6 ] 
[ 1, 6, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 1)
(1 1 1 0 1 0 0 1)
(0 0 1 0 1 0 0 1)
(0 1 0 1 1 0 0 1)
(0 1 0 0 1 0 0 1)
(0 1 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  887    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  277    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  401    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  370    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra  888    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  889    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  890    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 401

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 1, 6 ] 
[ 1, 6, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  915    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  287    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  344    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  380    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  916    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  917    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  814    permutation [ 8, 6, 1, 7, 2, 4, 5, 3 ]

Algebra 435

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 2, 3, 8, 4, 1 ] 
[ 3, 8, 4, 1, 2 ] 
[ 8, 4, 1, 2, 3 ] 
[ 1, 2, 3, 8, 4 ] 
[ 4, 1, 2, 3, 8 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(0 1 1 1 1 1 1 1)
(1 0 1 1 1 1 1 1)
(1 1 1 1 1 1 1 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  4 -> Algebra  951    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  947    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 492

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 5, 1 ] 
[ 4, 5, 8, 3 ] 
[ 5, 8, 3, 4 ] 
[ 1, 2, 5 ] 
[ 2, 5, 8 ] 
[ 3, 4, 5, 8 ] 
[ 5, 1, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 3, 4, 5 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 0 0 0)
(1 0 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(1 1 1 0 1 0 0 1)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  792    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  182    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  503    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  735    permutation [ 1, 3, 4, 5, 2, 6, 7, 8 ]
vertex  7 -> Algebra  995    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  921    permutation [ 3, 5, 1, 6, 7, 2, 4, 8 ]

Algebra 494

Quiver

[ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 8, 3, 4, 5, 2 ] 
[ 4, 5, 2, 8, 3 ] 
[ 5, 2, 8, 3, 4 ] 
[ 5, 2, 6 ] 
[ 3, 4, 5, 2, 8 ] 
[ 2, 6, 5 ] - [ 2, 8, 3, 4, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 0 1)
(1 1 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(1 1 1 0 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  335    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  995    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  505    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  182    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1000    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 495

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 5, 2 ] 
[ 4, 5, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 2, 3, 4 ] 
[ 5, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 4, 5, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 1 0)
(1 1 1 1 1 0 0 1)
(1 1 0 1 1 0 0 0)
(1 1 1 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  336    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  918    permutation [ 3, 5, 8, 6, 7, 1, 4, 2 ]
vertex  7 -> Algebra 1000    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  182    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 503

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 4, 1 ] 
[ 1, 2, 4 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 1 0 0 0)
(1 0 1 1 0 0 0 0)
(1 1 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  816    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  186    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  492    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  703    permutation [ 1, 3, 4, 5, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1013    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1014    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 504

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 8, 3, 4, 6, 2 ] 
[ 5, 3, 4 ] 
[ 6, 2, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 6, 2, 7 ] 
[ 3, 4, 6, 2, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 2, 8, 3 ] 
[ 2, 7, 6 ] - [ 2, 8, 3, 4, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 1 1 1)
(1 1 1 1 0 1 0 0)
(1 1 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(1 1 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra  345    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1015    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  507    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  6 -> Algebra  186    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 505

Quiver

[ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 6 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 5, 3 ] 
[ 2, 6, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 1 0 1)
(1 1 1 1 0 0 0 0)
(1 1 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 0 0 1 1 1 0 0)
(0 0 0 1 1 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  346    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1013    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  494    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  186    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 507

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 4 ], [ 8, 3 ]

Relations

[ 7, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 4, 2, 7 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 6, 3 ] 
[ 2, 7, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 0 1 1)
(1 1 1 1 0 0 0 0)
(1 1 1 1 0 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 0 0 1 0 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  348    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1022    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  513    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  504    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra  755    permutation [ 4, 2, 1, 8, 3, 6, 5, 7 ]

Algebra 513

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 7, 4 ], [ 8, 3 ]

Relations

[ 7, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 7 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 5, 3 ] 
[ 2, 7, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 0 1 1)
(1 1 1 1 0 0 0 0)
(1 1 1 1 1 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 1 1 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  354    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1031    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  507    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  314    permutation [ 4, 2, 1, 8, 3, 5, 6, 7 ]

Algebra 528

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 8, 3, 5, 6, 2 ] 
[ 4, 8, 3 ] 
[ 5, 6, 2, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 2, 8, 3, 5 ] 
[ 6, 2, 7 ] 
[ 2, 7, 6 ] - [ 2, 8, 3, 5, 6 ] 
[ 3, 4, 8 ] - [ 3, 5, 6, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 1 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 1)
(1 1 0 0 1 1 0 1)
(1 1 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  371    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1047    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1049    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 649

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 5, 1 ] 
[ 8, 3, 4, 5, 1 ] 
[ 4, 5, 1, 8, 3 ] 
[ 5, 1, 8, 3, 4 ] 
[ 5, 1, 6 ] 
[ 3, 4, 5, 1, 8 ] 
[ 1, 6, 5 ] - [ 1, 8, 3, 4, 5 ] 

Cartan matrix

(1 0 1 1 1 1 0 1)
(1 1 1 1 1 0 0 0)
(1 0 1 1 1 0 0 0)
(1 0 0 1 1 0 0 1)
(1 0 1 0 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  755    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  679    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  656    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  258    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  348    permutation [ 2, 3, 5, 1, 7, 6, 8, 4 ]

Algebra 653

Quiver

[ 1, 5 ], [ 2, 4 ], [ 2, 8 ], [ 3, 1 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 4, 3, 1 ] 
[ 4, 3, 2 ] 
[ 8, 3, 2 ] 
[ 1, 5, 4, 3 ] 
[ 4, 3, 1, 5 ] 
[ 3, 2, 8 ] 
[ 2, 4, 3 ] - [ 2, 8, 3 ] 
[ 3, 1, 5, 4 ] - [ 3, 2, 4 ] 

Cartan matrix

(1 0 0 1 1 1 1 0)
(1 1 1 1 0 0 0 1)
(1 1 1 1 1 1 1 0)
(1 0 1 1 0 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  725    permutation [ 2, 1, 3, 5, 6, 7, 8, 4 ]
vertex  2 -> Algebra 1163    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  307    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  837    permutation [ 2, 3, 5, 1, 6, 7, 8, 4 ]
vertex  7 -> Algebra  927    permutation [ 2, 3, 1, 5, 7, 6, 8, 4 ]
vertex  8 -> Algebra  276    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 655

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 1 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 1 ] 
[ 8, 3, 4, 6, 1 ] 
[ 5, 3, 4 ] 
[ 6, 1, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 6, 1, 7 ] 
[ 3, 4, 6, 1, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 1, 8, 3 ] 
[ 1, 7, 6 ] - [ 1, 8, 3, 4, 6 ] 

Cartan matrix

(1 0 1 1 0 1 1 1)
(1 1 1 1 0 1 0 0)
(1 0 1 1 0 1 0 0)
(1 0 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(1 0 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 1 0 1 0 1)

Good mutations

vertex  2 -> Algebra  761    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  707    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  658    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  6 -> Algebra  262    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 656

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 3 ], [ 6, 4 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 4, 1 ] 
[ 8, 3, 4, 1 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 1, 6 ] 
[ 3, 4, 1, 8 ] 
[ 4, 1, 8, 3 ] - [ 4, 5, 3 ] 
[ 1, 6, 4 ] - [ 1, 8, 3, 4 ] 

Cartan matrix

(1 0 1 1 0 1 0 1)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 0 0 1 1 1 0 0)
(0 0 0 1 1 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  762    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  708    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  649    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  262    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 658

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 6 ], [ 5, 6 ], [ 6, 3 ], [ 7, 4 ], [ 8, 3 ]

Relations

[ 7, 4, 1 ] 
[ 8, 3, 4, 1 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 4, 1, 7 ] 
[ 3, 4, 1, 8 ] 
[ 4, 1, 8, 3 ] - [ 4, 6, 3 ] 
[ 1, 7, 4 ] - [ 1, 8, 3, 4 ] 

Cartan matrix

(1 0 1 1 0 0 1 1)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 0 1 1 0 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 0 0 1 0 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  764    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  716    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  664    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  655    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra 1170    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 664

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 7, 4 ], [ 8, 3 ]

Relations

[ 7, 4, 1 ] 
[ 8, 3, 4, 1 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 1, 7 ] 
[ 3, 4, 1, 8 ] 
[ 4, 1, 8, 3 ] - [ 4, 5, 3 ] 
[ 1, 7, 4 ] - [ 1, 8, 3, 4 ] 

Cartan matrix

(1 0 1 1 0 0 1 1)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 0 1 1 1 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 1 1 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  770    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  725    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  658    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1175    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 679

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 8 ], [ 5, 1 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 5, 1 ] 
[ 8, 3, 5, 1 ] 
[ 3, 4, 2 ] 
[ 5, 1, 8, 3 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 5, 1, 6 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 1, 6, 5 ] - [ 1, 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 1, 8 ] 

Cartan matrix

(1 0 1 0 1 1 0 1)
(1 1 1 0 1 0 0 0)
(1 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(1 0 0 0 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 0 1 0 0 1)

Good mutations

vertex  2 -> Algebra  858    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  689    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra  649    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  275    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  273    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1188    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 680

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 3 ], [ 3, 5 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 6, 5, 1 ] 
[ 3, 8, 4, 2 ] 
[ 5, 1, 3 ] 
[ 2, 3, 8, 4 ] 
[ 5, 1, 6 ] 
[ 1, 3, 8 ] 
[ 4, 2, 3, 8 ] 
[ 3, 5, 1 ] - [ 3, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 4, 2, 3 ] 
[ 1, 3, 5 ] - [ 1, 6, 5 ] 

Cartan matrix

(1 0 1 0 1 1 1 0)
(1 1 1 0 1 0 0 1)
(1 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 0)
(1 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1189    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  859    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1190    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  837    permutation [ 2, 8, 5, 1, 6, 7, 4, 3 ]
vertex  5 -> Algebra  276    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1188    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  273    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 682

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 5, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 3, 1, 5 ] 
[ 1, 5, 3 ] - [ 1, 8, 3 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 1 0 1 0 0 1)
(1 1 1 0 0 0 0 0)
(1 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 1 1 1 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  861    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  684    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1195    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 684

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 3, 1, 5 ] 
[ 1, 5, 3 ] - [ 1, 8, 3 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 1 0 1 0 0 1)
(1 1 1 0 0 0 0 0)
(1 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  863    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  275    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  682    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1014    permutation [ 1, 5, 2, 8, 4, 6, 7, 3 ]

Algebra 685

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 1 ] 
[ 3, 8, 4, 2 ] 
[ 2, 3, 8, 4 ] 
[ 3, 8, 1, 5 ] 
[ 1, 5, 3, 8 ] 
[ 4, 2, 3, 8 ] 
[ 8, 1, 5, 3 ] - [ 8, 4, 2, 3 ] 

Cartan matrix

(1 0 1 0 1 1 0 0)
(1 1 1 0 0 0 0 1)
(1 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 0)
(0 0 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1197    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  864    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  703    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  927    permutation [ 2, 8, 1, 5, 7, 6, 4, 3 ]
vertex  5 -> Algebra 1188    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1014    permutation [ 1, 5, 2, 8, 4, 6, 7, 3 ]
vertex  7 -> Algebra  276    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  275    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 686

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 8, 5, 1 ] 
[ 3, 8, 4, 2 ] 
[ 2, 3, 8, 4 ] 
[ 1, 8, 5 ] 
[ 3, 8, 5 ] 
[ 4, 2, 3, 8 ] 
[ 8, 4, 2, 3 ] - [ 8, 5, 3 ] 
[ 5, 1, 8 ] - [ 5, 3, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 0)
(1 0 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  276    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  704    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  725    permutation [ 2, 1, 8, 5, 6, 7, 4, 3 ]
vertex  5 -> Algebra 1175    permutation [ 2, 1, 5, 8, 6, 7, 4, 3 ]
vertex  7 -> Algebra 1197    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 688

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 2 ], [ 5, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 1 ] 
[ 8, 3, 6, 1 ] 
[ 3, 5, 2 ] 
[ 6, 1, 8, 3 ] 
[ 2, 3, 5 ] 
[ 8, 3, 5 ] 
[ 6, 1, 7 ] 
[ 5, 2, 3 ] - [ 5, 8, 3 ] 
[ 1, 7, 6 ] - [ 1, 8, 3, 6 ] 
[ 3, 5, 8 ] - [ 3, 6, 1, 8 ] 

Cartan matrix

(1 0 1 0 0 1 1 1)
(1 1 1 0 0 1 0 0)
(1 0 1 0 1 1 0 1)
(0 1 1 1 1 1 0 1)
(0 1 1 0 1 1 0 1)
(1 0 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 1 0 1)

Good mutations

vertex  2 -> Algebra  888    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  691    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra  707    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  277    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1202    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 689

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 5, 8 ], [ 6, 3 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 5, 2 ] 
[ 2, 3, 5 ] 
[ 8, 3, 5 ] 
[ 3, 1, 6 ] 
[ 1, 6, 3 ] - [ 1, 8, 3 ] 
[ 5, 2, 3 ] - [ 5, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 0 1 0 0 1 0 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 1 0 0 1)
(0 1 1 1 1 0 0 1)
(0 1 1 0 1 0 0 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 1 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  889    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  708    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  679    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra  277    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1204    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 690

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 3 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 6, 3, 8, 1 ] 
[ 3, 8, 5, 2 ] 
[ 2, 3, 8, 5 ] 
[ 3, 8, 1, 6 ] 
[ 1, 6, 3, 8 ] 
[ 5, 2, 3, 8 ] 
[ 8, 1, 6, 3 ] - [ 8, 5, 2, 3 ] 

Cartan matrix

(1 0 1 0 0 1 1 0)
(1 1 1 0 0 0 0 1)
(1 0 1 0 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 0 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1205    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  890    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  696    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  709    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1190    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1202    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1204    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  277    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 691

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 6 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 6, 8 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 7, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 6, 2 ] 
[ 2, 3, 6 ] 
[ 8, 3, 6 ] 
[ 3, 1, 7 ] 
[ 1, 7, 3 ] - [ 1, 8, 3 ] 
[ 6, 2, 3 ] - [ 6, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 0 1 0 0 0 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 1 0 1)
(0 1 1 1 1 1 0 1)
(0 1 1 0 1 1 0 1)
(0 1 1 0 0 1 0 1)
(0 0 1 0 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  896    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  710    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  688    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra 1207    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1208    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 696

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 3 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 6, 3, 1 ] 
[ 1, 6, 3 ] 
[ 5, 2, 3 ] 
[ 2, 3, 5 ] 
[ 2, 3, 8 ] 
[ 6, 3, 8 ] 
[ 3, 5, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 6, 3 ] 
[ 3, 1, 6 ] - [ 3, 8, 6 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 1 0 0 0 0 0)
(1 1 1 0 1 1 1 1)
(0 1 0 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1211    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  715    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  705    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra  785    permutation [ 3, 8, 1, 7, 2, 5, 4, 6 ]
vertex  7 -> Algebra 1022    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra  690    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 703

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 5, 3, 1 ] 
[ 1, 5, 3 ] 
[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 2, 3, 8 ] 
[ 5, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 5, 3 ] 
[ 3, 1, 5 ] - [ 3, 8, 5 ] 

Cartan matrix

(1 0 0 0 1 1 0 0)
(1 1 1 0 0 0 0 0)
(1 1 1 1 1 1 0 1)
(0 1 0 1 0 0 0 0)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1217    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  735    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1015    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  6 -> Algebra  503    permutation [ 1, 5, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  286    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  685    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 704

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 3, 8, 5, 1 ] 
[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 1, 3, 8, 5 ] 
[ 2, 3, 8 ] 
[ 5, 1, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 5, 1, 3 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 1 1 1 1 1 1 1)
(0 1 0 1 0 0 0 0)
(1 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  286    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  911    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  737    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1218    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1217    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  686    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 705

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 6, 5, 1 ] 
[ 4, 2, 3 ] 
[ 5, 8, 2, 3 ] 
[ 2, 3, 4 ] 
[ 1, 6, 5 ] 
[ 2, 3, 5, 8 ] 
[ 6, 5, 8 ] 
[ 3, 4, 2 ] - [ 3, 5, 8, 2 ] 
[ 8, 2, 3, 5 ] - [ 8, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 1 0 1 0 0 0)
(1 1 1 1 1 1 1 1)
(0 1 0 1 0 0 0 0)
(1 1 0 0 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1219    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  696    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra  286    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1015    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1190    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 707

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 1 ] 
[ 8, 3, 6, 1 ] 
[ 3, 4, 2 ] 
[ 6, 1, 8, 3 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 6, 1, 7 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 1, 7, 6 ] - [ 1, 8, 3, 6 ] 
[ 3, 4, 8 ] - [ 3, 6, 1, 8 ] 

Cartan matrix

(1 0 1 0 0 1 1 1)
(1 1 1 0 0 1 0 0)
(1 0 1 1 1 1 0 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(1 0 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 1 0 1)

Good mutations

vertex  2 -> Algebra  916    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  710    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra  655    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  688    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  287    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  795    permutation [ 8, 2, 1, 7, 6, 4, 5, 3 ]

Algebra 708

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 6, 3 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 3, 1, 6 ] 
[ 1, 6, 3 ] - [ 1, 8, 3 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 1 0 0 1 0 1)
(1 1 1 0 0 0 0 0)
(1 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 0 0)
(0 0 1 1 1 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  917    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  656    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  689    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  287    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1226    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 709

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 6, 3, 8, 1 ] 
[ 3, 8, 4, 2 ] 
[ 2, 3, 8, 4 ] 
[ 3, 8, 1, 6 ] 
[ 1, 6, 3, 8 ] 
[ 4, 2, 3, 8 ] 
[ 8, 1, 6, 3 ] - [ 8, 4, 2, 3 ] 

Cartan matrix

(1 0 1 0 0 1 1 0)
(1 1 1 0 0 0 0 1)
(1 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1227    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  814    permutation [ 8, 6, 1, 7, 3, 4, 5, 2 ]
vertex  3 -> Algebra  715    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  5 -> Algebra  690    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  795    permutation [ 8, 2, 1, 7, 6, 4, 5, 3 ]
vertex  7 -> Algebra 1226    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  287    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 710

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 6 ], [ 4, 5 ], [ 4, 6 ], [ 6, 2 ], [ 6, 8 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 7, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 6, 2 ] 
[ 2, 3, 6 ] 
[ 8, 3, 6 ] 
[ 3, 1, 7 ] 
[ 1, 7, 3 ] - [ 1, 8, 3 ] 
[ 6, 2, 3 ] - [ 6, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 0 1 0 0 0 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 1 0 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(0 1 1 0 0 1 0 1)
(0 0 1 0 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  921    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  716    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra  691    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  707    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra 1229    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  792    permutation [ 6, 2, 1, 7, 3, 4, 5, 8 ]

Algebra 715

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 6, 3, 1 ] 
[ 1, 6, 3 ] 
[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 2, 3, 8 ] 
[ 6, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 6, 3 ] 
[ 3, 1, 6 ] - [ 3, 8, 6 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 1 0 0 0 0 0)
(1 1 1 1 1 1 1 1)
(0 1 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1231    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  696    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  329    permutation [ 3, 8, 1, 7, 2, 4, 5, 6 ]
vertex  7 -> Algebra 1031    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra  709    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 716

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 7, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 3, 1, 7 ] 
[ 1, 7, 3 ] - [ 1, 8, 3 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 1 0 0 0 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 1 0 1 0 1)
(0 1 1 1 0 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  927    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  658    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  725    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  710    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra 1197    permutation [ 2, 1, 8, 7, 4, 6, 5, 3 ]
vertex  8 -> Algebra 1233    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 725

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 5, 6 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 7, 3, 1 ] 
[ 8, 3, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 3, 1, 7 ] 
[ 1, 7, 3 ] - [ 1, 8, 3 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 1 0 0 0 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 1 1 1 0 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 1 1 1 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  653    permutation [ 2, 1, 3, 8, 4, 5, 6, 7 ]
vertex  4 -> Algebra  664    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  716    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  686    permutation [ 2, 1, 8, 7, 4, 5, 6, 3 ]
vertex  8 -> Algebra  737    permutation [ 2, 1, 7, 3, 4, 5, 6, 8 ]

Algebra 735

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 5, 4, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 1, 5, 4 ] 
[ 2, 3, 4, 8 ] 
[ 5, 4, 8 ] 
[ 8, 2, 3, 4 ] - [ 8, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 8, 5 ] 

Cartan matrix

(1 0 0 0 1 1 0 0)
(1 1 1 1 0 0 0 0)
(1 0 1 1 1 1 0 1)
(1 1 0 1 1 1 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1233    permutation [ 2, 1, 4, 5, 7, 6, 3, 8 ]
vertex  3 -> Algebra  703    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  492    permutation [ 1, 5, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  307    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  927    permutation [ 2, 4, 1, 5, 7, 6, 3, 8 ]

Algebra 736

Quiver

[ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 3, 8, 1 ] 
[ 4, 8, 1 ] 
[ 3, 8, 2 ] 
[ 4, 8, 5 ] 
[ 2, 3, 8 ] 
[ 5, 4, 8 ] 
[ 8, 1, 3 ] - [ 8, 2, 3 ] 
[ 8, 1, 4 ] - [ 8, 5, 4 ] 
[ 1, 3, 8 ] - [ 1, 4, 8 ] 

Cartan matrix

(1 0 1 1 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 0 1 1 1 1)
(0 1 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  737    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  2 -> Algebra  951    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1234    permutation [ 2, 4, 8, 5, 7, 6, 3, 1 ]

Algebra 737

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 4, 8, 5, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 1, 4, 8, 5 ] 
[ 2, 3, 4, 8 ] 
[ 5, 1, 4, 8 ] 
[ 8, 2, 3, 4 ] - [ 8, 5, 1, 4 ] 

Cartan matrix

(1 1 0 1 0 0 0 1)
(0 1 1 1 0 0 0 0)
(0 0 1 1 1 1 1 1)
(0 1 0 1 1 1 1 1)
(1 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  307    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  952    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  704    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  736    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1233    permutation [ 2, 1, 4, 5, 7, 6, 3, 8 ]
vertex  8 -> Algebra  725    permutation [ 2, 1, 4, 5, 6, 7, 3, 8 ]

Algebra 755

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 5, 1 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 6, 5, 1 ] 
[ 8, 2, 4, 5, 1 ] 
[ 4, 5, 1, 8, 2 ] 
[ 5, 1, 8, 2, 4 ] 
[ 5, 1, 6 ] 
[ 2, 4, 5, 1, 8 ] 
[ 1, 6, 5 ] - [ 1, 8, 2, 4, 5 ] 

Cartan matrix

(1 1 1 1 1 1 0 1)
(1 1 1 1 1 0 0 0)
(0 0 1 0 0 0 0 0)
(1 0 0 1 1 0 0 1)
(1 1 1 0 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  785    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  649    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  762    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  314    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  507    permutation [ 3, 2, 5, 1, 7, 6, 8, 4 ]

Algebra 761

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 2 ], [ 6, 1 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 7, 6, 1 ] 
[ 8, 2, 4, 6, 1 ] 
[ 5, 2, 4 ] 
[ 6, 1, 8, 2, 4 ] 
[ 2, 4, 5 ] 
[ 6, 1, 7 ] 
[ 2, 4, 6, 1, 8 ] 
[ 4, 5, 2 ] - [ 4, 6, 1, 8, 2 ] 
[ 1, 7, 6 ] - [ 1, 8, 2, 4, 6 ] 

Cartan matrix

(1 1 1 1 0 1 1 1)
(1 1 1 1 0 1 0 0)
(0 0 1 0 0 0 0 0)
(1 1 1 1 1 1 0 1)
(0 1 1 0 1 0 0 0)
(1 1 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 1 0 1 0 1)

Good mutations

vertex  2 -> Algebra  817    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  655    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  764    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  6 -> Algebra  318    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 762

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 6, 4 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 6, 4, 1 ] 
[ 8, 2, 4, 1 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 4, 1, 6 ] 
[ 2, 4, 1, 8 ] 
[ 4, 1, 8, 2 ] - [ 4, 5, 2 ] 
[ 1, 6, 4 ] - [ 1, 8, 2, 4 ] 

Cartan matrix

(1 1 1 1 0 1 0 1)
(1 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(1 1 1 1 1 0 0 1)
(0 1 1 0 1 0 0 0)
(0 0 0 1 1 1 0 0)
(0 0 0 1 1 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  818    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  656    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  755    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  318    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 764

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 4, 6 ], [ 5, 6 ], [ 6, 2 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 7, 4, 1 ] 
[ 8, 2, 4, 1 ] 
[ 6, 2, 4 ] 
[ 2, 4, 6 ] 
[ 4, 1, 7 ] 
[ 2, 4, 1, 8 ] 
[ 4, 1, 8, 2 ] - [ 4, 6, 2 ] 
[ 1, 7, 4 ] - [ 1, 8, 2, 4 ] 

Cartan matrix

(1 1 1 1 0 0 1 1)
(1 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(1 1 1 1 0 1 0 1)
(0 1 1 0 1 1 0 0)
(0 1 1 0 0 1 0 0)
(0 0 0 1 0 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  827    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  658    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  770    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  761    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra 1260    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 770

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 7, 4, 1 ] 
[ 8, 2, 4, 1 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 4, 1, 7 ] 
[ 2, 4, 1, 8 ] 
[ 4, 1, 8, 2 ] - [ 4, 5, 2 ] 
[ 1, 7, 4 ] - [ 1, 8, 2, 4 ] 

Cartan matrix

(1 1 1 1 0 0 1 1)
(1 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(1 1 1 1 1 1 0 1)
(0 1 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 1 1 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  837    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  664    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  764    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1189    permutation [ 2, 1, 8, 7, 3, 5, 6, 4 ]

Algebra 783

Quiver

[ 1, 5 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 5, 8, 1 ] 
[ 4, 8, 2 ] 
[ 5, 8, 2 ] 
[ 4, 8, 3 ] 
[ 1, 5, 8 ] 
[ 3, 4, 8 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 8, 1, 5 ] - [ 8, 2, 5 ] 
[ 2, 4, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 1 0 0 0)
(0 1 0 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(1 0 0 1 0 0 0 1)
(0 0 1 0 1 0 0 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  329    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  792    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  856    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1234    permutation [ 3, 5, 8, 1, 7, 6, 4, 2 ]
vertex  7 -> Algebra 1210    permutation [ 3, 5, 8, 7, 6, 1, 4, 2 ]

Algebra 785

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 5, 1 ] 
[ 8, 2, 5, 1 ] 
[ 4, 8, 2 ] 
[ 5, 1, 8, 2 ] 
[ 4, 8, 3 ] 
[ 5, 1, 6 ] 
[ 3, 4, 8 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 1, 6, 5 ] - [ 1, 8, 2, 5 ] 
[ 2, 4, 8 ] - [ 2, 5, 1, 8 ] 

Cartan matrix

(1 1 1 1 1 1 0 1)
(1 1 0 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(0 0 0 1 0 0 0 1)
(1 0 1 0 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1210    permutation [ 3, 5, 8, 7, 6, 1, 4, 2 ]
vertex  2 -> Algebra  794    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  858    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  755    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  7 -> Algebra  329    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  696    permutation [ 3, 5, 1, 7, 6, 8, 4, 2 ]

Algebra 791

Quiver

[ 1, 5 ], [ 2, 8 ], [ 3, 1 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 5, 2, 8, 3, 1 ] 
[ 8, 3, 1, 5, 2 ] 
[ 1, 5, 2, 8, 3 ] 
[ 2, 8, 3, 1, 5 ] 
[ 3, 1, 5, 2, 8 ] 

Cartan matrix

(1 1 0 1 1 1 1 1)
(1 1 1 1 0 0 0 1)
(1 1 1 0 1 1 1 0)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 1 1 1 1 1)

Good mutations

vertex  4 -> Algebra 1163    permutation [ 1, 8, 3, 2, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1231    permutation [ 3, 5, 1, 6, 7, 8, 4, 2 ]
vertex  7 -> Algebra 1277    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  369    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 792

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 5, 8, 1 ] 
[ 5, 8, 1, 2 ] 
[ 4, 5, 8, 3 ] 
[ 5, 8, 3, 4 ] 
[ 1, 2, 5, 8 ] 
[ 3, 4, 5, 8 ] 
[ 8, 1, 2, 5 ] - [ 8, 3, 4, 5 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 1 0 1 0 0 1)
(0 0 1 1 1 0 0 0)
(1 0 0 1 1 0 0 1)
(1 0 1 0 1 0 0 1)
(1 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  333    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  492    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  866    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  816    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  783    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1233    permutation [ 3, 2, 5, 1, 7, 6, 4, 8 ]
vertex  7 -> Algebra 1208    permutation [ 3, 2, 5, 7, 6, 1, 4, 8 ]
vertex  8 -> Algebra  710    permutation [ 3, 2, 5, 6, 7, 1, 4, 8 ]

Algebra 794

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 2, 1 ] 
[ 8, 2, 1 ] 
[ 5, 8, 2 ] 
[ 4, 5, 8, 3 ] 
[ 5, 8, 3, 4 ] 
[ 2, 1, 6 ] 
[ 3, 4, 5, 8 ] 
[ 1, 6, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 3, 4, 5 ] 
[ 2, 1, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 1 1 1 1 1 0 1)
(1 1 1 0 1 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 0 1 1 0 0 1)
(0 0 1 0 1 0 0 1)
(0 1 0 0 1 1 0 0)
(0 1 0 0 1 1 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1208    permutation [ 3, 2, 5, 7, 6, 1, 4, 8 ]
vertex  2 -> Algebra  335    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  868    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  818    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  785    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra  333    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1202    permutation [ 3, 2, 8, 7, 6, 5, 4, 1 ]

Algebra 795

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 8 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 3, 8, 1 ] 
[ 6, 2, 8, 1 ] 
[ 8, 1, 6, 2 ] 
[ 4, 5, 3 ] 
[ 5, 3, 4 ] 
[ 2, 8, 1, 6 ] 
[ 5, 3, 8 ] 
[ 8, 1, 3 ] - [ 8, 5, 3 ] 
[ 3, 4, 5 ] - [ 3, 8, 5 ] 
[ 1, 3, 8 ] - [ 1, 6, 2, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 1 0 1 0 0 1)
(0 0 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 1 0 1 0 0 0)
(0 1 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 0 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  707    permutation [ 3, 2, 8, 6, 7, 5, 4, 1 ]
vertex  2 -> Algebra  801    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1282    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  709    permutation [ 3, 2, 8, 6, 7, 5, 4, 1 ]
vertex  7 -> Algebra 1202    permutation [ 3, 2, 8, 7, 6, 5, 4, 1 ]
vertex  8 -> Algebra  333    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 800

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 6, 5, 2 ] 
[ 4, 5, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 2, 3, 4 ] 
[ 5, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 4, 5, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 1 1 1 1 1 0 0)
(0 1 1 1 1 1 0 0)
(0 1 1 1 1 0 0 1)
(0 1 0 1 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1000    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1290    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1289    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  336    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  335    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 801

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 3, 2, 1 ] 
[ 6, 2, 1 ] 
[ 5, 3, 2 ] 
[ 8, 6, 2 ] 
[ 4, 5, 3 ] 
[ 5, 3, 4 ] 
[ 6, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 6, 2 ] 
[ 2, 1, 3 ] - [ 2, 5, 3 ] 
[ 3, 2, 5 ] - [ 3, 4, 5 ] 
[ 2, 1, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(1 1 1 0 1 1 1 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 1 0 1 0 0 0)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  916    permutation [ 3, 2, 8, 6, 7, 5, 4, 1 ]
vertex  2 -> Algebra  336    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  814    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1290    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  795    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 814

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 4 ], [ 2, 5 ], [ 3, 2 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 3, 2, 5, 1 ] 
[ 6, 5, 1 ] 
[ 5, 1, 3, 2 ] 
[ 2, 5, 1, 3 ] 
[ 8, 6, 5 ] 
[ 6, 5, 8 ] 
[ 1, 3, 2, 5 ] - [ 1, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 0 1 0 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  401    permutation [ 3, 5, 8, 6, 7, 2, 4, 1 ]
vertex  2 -> Algebra  801    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  4 -> Algebra  851    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  7 -> Algebra  890    permutation [ 3, 5, 8, 7, 6, 2, 4, 1 ]
vertex  8 -> Algebra  709    permutation [ 3, 8, 5, 6, 7, 2, 4, 1 ]

Algebra 816

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 1 1 0 0 0)
(0 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(1 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(1 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  344    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  503    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  915    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  792    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1217    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]
vertex  7 -> Algebra 1309    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1229    permutation [ 3, 2, 4, 6, 7, 1, 5, 8 ]

Algebra 817

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 4 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 1 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 6, 1 ] 
[ 8, 2, 6, 1 ] 
[ 4, 8, 2 ] 
[ 6, 1, 8, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 6, 1, 7 ] 
[ 3, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 1, 7, 6 ] - [ 1, 8, 2, 6 ] 
[ 2, 4, 8 ] - [ 2, 6, 1, 8 ] 

Cartan matrix

(1 1 1 1 0 1 1 1)
(1 1 1 1 1 1 0 1)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(1 0 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1310    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  820    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra  916    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  761    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra  344    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 818

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 2, 1 ] 
[ 8, 2, 1 ] 
[ 4, 8, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 1, 6 ] 
[ 3, 4, 8 ] 
[ 1, 6, 2 ] - [ 1, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 1, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 1 0 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 1 0 1 1 1 0 0)
(0 1 0 1 1 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1309    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  346    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  917    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  762    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra  794    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  344    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 820

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 6, 8, 2 ] 
[ 5, 3, 4 ] 
[ 6, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 1, 7 ] 
[ 3, 4, 6, 8 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 6, 8, 3 ] 
[ 8, 2, 6 ] - [ 8, 3, 4, 6 ] 
[ 2, 1, 8 ] - [ 2, 6, 8 ] 

Cartan matrix

(1 1 1 1 0 1 1 1)
(1 1 1 0 0 1 0 1)
(0 0 1 1 0 1 0 0)
(0 0 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(0 0 1 0 0 1 0 1)
(0 1 0 0 0 1 1 0)
(0 1 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1314    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  345    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  918    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  827    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  6 -> Algebra  817    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]

Algebra 827

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 4, 8, 2 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 2, 1, 7 ] 
[ 3, 4, 8 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 4, 6, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 1, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 0 1 1)
(1 1 1 1 0 1 0 1)
(0 0 1 1 0 0 0 0)
(0 0 1 1 0 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 1 0 1 0 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1324    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  348    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  927    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  764    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra  837    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  820    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra 1188    permutation [ 4, 1, 8, 7, 3, 6, 5, 2 ]

Algebra 837

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 4, 8, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 1, 7 ] 
[ 3, 4, 8 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 1, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 0 1 1)
(1 1 1 1 1 1 0 1)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 1 0 1 1 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1336    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  354    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  653    permutation [ 4, 1, 2, 8, 3, 5, 6, 7 ]
vertex  4 -> Algebra  770    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra  827    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  680    permutation [ 4, 1, 8, 7, 3, 5, 6, 2 ]

Algebra 851

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 3, 4, 5, 1 ] 
[ 6, 5, 1 ] 
[ 4, 5, 1, 3 ] 
[ 5, 1, 3, 4 ] 
[ 8, 6, 5 ] 
[ 6, 5, 8 ] 
[ 1, 3, 4, 5 ] - [ 1, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 0 1 1 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 0 1 1 1 0 0 1)
(1 0 0 1 1 1 1 1)
(1 0 1 0 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  917    permutation [ 3, 5, 8, 6, 7, 4, 2, 1 ]
vertex  2 -> Algebra  814    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1349    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1226    permutation [ 3, 8, 5, 6, 7, 4, 2, 1 ]

Algebra 852

Quiver

[ 1, 2 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 2, 3, 4, 8, 1 ] 
[ 3, 4, 8, 1, 2 ] 
[ 4, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 4 ] 
[ 1, 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(0 1 1 1 0 0 0 1)
(1 0 1 1 1 0 0 1)
(1 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  856    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  5 -> Algebra  365    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  947    permutation [ 2, 3, 4, 1, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1354    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 854

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ]

Relations

[ 2, 3, 4, 8, 1 ] 
[ 3, 4, 8, 1, 2 ] 
[ 4, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 4 ] 
[ 1, 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 0 0 0 1)
(1 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  368    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1354    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1358    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  365    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 856

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 5, 8, 1 ] 
[ 3, 4, 8, 2 ] 
[ 5, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 1, 5, 8 ] 
[ 8, 1, 5 ] - [ 8, 2, 5 ] 
[ 2, 3, 4, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 1 0 0 0)
(0 1 1 1 1 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  366    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  866    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  4 -> Algebra  783    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  852    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  6 -> Algebra 1360    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1361    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 858

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 6, 5, 1 ] 
[ 8, 2, 5, 1 ] 
[ 3, 4, 8, 2 ] 
[ 5, 1, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 5, 1, 6 ] 
[ 1, 6, 5 ] - [ 1, 8, 2, 5 ] 
[ 2, 3, 4, 8 ] - [ 2, 5, 1, 8 ] 

Cartan matrix

(1 1 1 0 1 1 0 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 1 0 0 1)
(1 0 0 0 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1361    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  868    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  679    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  785    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  368    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  366    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1367    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 859

Quiver

[ 1, 2 ], [ 1, 6 ], [ 2, 3 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 6, 5, 1 ] 
[ 3, 4, 2 ] 
[ 5, 1, 2 ] 
[ 4, 2, 3 ] 
[ 5, 1, 6 ] 
[ 1, 2, 8 ] 
[ 4, 2, 8 ] 
[ 2, 5, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 2 ] - [ 8, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 
[ 1, 2, 5 ] - [ 1, 6, 5 ] 

Cartan matrix

(1 1 1 0 1 1 1 0)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 1 0 0 0)
(1 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1369    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  680    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1231    permutation [ 8, 5, 1, 6, 7, 4, 3, 2 ]
vertex  5 -> Algebra  369    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1367    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  366    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 861

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 5, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 1, 5 ] 
[ 1, 5, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(1 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 0 0 0 1)
(0 1 1 1 1 0 0 0)
(0 1 1 1 1 1 1 0)
(0 1 1 1 1 0 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1356    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  682    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  863    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1374    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 863

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 5, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 1, 5 ] 
[ 1, 5, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(1 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 0 0 0 1)
(0 1 1 1 1 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1358    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  684    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  368    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  861    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1377    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 864

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 5, 2, 8, 1 ] 
[ 3, 4, 2 ] 
[ 4, 2, 3 ] 
[ 2, 8, 1, 5 ] 
[ 1, 5, 2, 8 ] 
[ 4, 2, 8 ] 
[ 8, 1, 5, 2 ] - [ 8, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 

Cartan matrix

(1 1 1 0 1 1 0 0)
(1 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 0 0 0 0)
(0 1 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  3 -> Algebra  685    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1277    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1367    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1377    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  369    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  368    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 866

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 5, 8, 1 ] 
[ 5, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 4 ] 
[ 1, 2, 5, 8 ] 
[ 8, 1, 2, 5 ] - [ 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 0 0 1 0 0 1)
(1 0 1 1 1 0 0 1)
(1 1 0 1 0 0 0 1)
(1 0 0 0 1 0 0 1)
(1 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  370    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  887    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra  792    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  856    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1380    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1381    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 868

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 2, 1 ] 
[ 8, 2, 1 ] 
[ 5, 8, 2 ] 
[ 4, 8, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 4 ] 
[ 2, 1, 6 ] 
[ 1, 6, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 3, 5 ] 
[ 2, 1, 8 ] - [ 2, 5, 8 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 1 1 0 1)
(1 1 0 0 1 0 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 0 0 0 1)
(0 0 0 0 1 0 0 1)
(0 1 0 0 1 1 0 0)
(0 1 0 0 1 1 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1381    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  889    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra  794    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  858    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra  370    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1387    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 869

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 6, 2 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 3, 8, 1 ] 
[ 6, 2, 8, 1 ] 
[ 8, 1, 3 ] 
[ 2, 8, 4 ] 
[ 2, 8, 1, 6 ] 
[ 4, 2, 8 ] 
[ 8, 1, 6, 2 ] - [ 8, 4, 2 ] 
[ 1, 3, 8 ] - [ 1, 6, 2, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(1 1 0 0 1 0 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  3 -> Algebra 1389    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1282    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1369    permutation [ 1, 8, 3, 4, 2, 6, 7, 5 ]
vertex  7 -> Algebra 1387    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  370    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 872

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 7 ], [ 3, 5 ], [ 3, 8 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 7, 6, 2 ] 
[ 5, 6, 2, 3 ] 
[ 8, 2, 3 ] 
[ 6, 2, 3, 5 ] 
[ 6, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 5, 6, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 5, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 1 1 0 1 1 1 0)
(0 1 1 0 1 1 1 0)
(0 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(0 1 0 0 1 1 0 0)
(0 1 1 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1049    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1218    permutation [ 1, 6, 3, 5, 7, 8, 4, 2 ]
vertex  4 -> Algebra 1287    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  7 -> Algebra 1175    permutation [ 6, 1, 2, 3, 8, 4, 5, 7 ]
vertex  8 -> Algebra  371    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 887

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 2, 3, 5, 8, 1 ] 
[ 3, 5, 8, 1, 2 ] 
[ 5, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 5 ] 
[ 1, 2, 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 0)
(0 1 1 0 1 0 0 1)
(1 0 1 0 1 0 0 1)
(1 1 0 1 1 0 0 1)
(1 1 0 0 1 0 0 1)
(1 1 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  380    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  915    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  866    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra 1410    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1411    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 888

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 7, 6, 1 ] 
[ 8, 2, 6, 1 ] 
[ 3, 5, 8, 2 ] 
[ 6, 1, 8, 2 ] 
[ 5, 8, 2, 3 ] 
[ 8, 2, 3, 5 ] 
[ 6, 1, 7 ] 
[ 1, 7, 6 ] - [ 1, 8, 2, 6 ] 
[ 2, 3, 5, 8 ] - [ 2, 6, 1, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 1)
(1 1 1 0 1 1 0 1)
(0 0 1 0 1 0 0 1)
(0 1 0 1 1 1 0 1)
(0 1 0 0 1 1 0 1)
(1 0 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1413    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  891    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra  688    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  916    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  380    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1290    permutation [ 8, 2, 1, 7, 6, 5, 4, 3 ]

Algebra 889

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 6, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 5, 8, 2 ] 
[ 5, 8, 2, 3 ] 
[ 8, 2, 3, 5 ] 
[ 2, 1, 6 ] 
[ 1, 6, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 0 1 0 1)
(1 1 1 0 1 0 0 1)
(0 0 1 0 1 0 0 1)
(0 1 0 1 1 0 0 1)
(0 1 0 0 1 0 0 1)
(0 1 1 0 1 1 0 0)
(0 1 1 0 1 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1411    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  689    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  917    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  868    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra  380    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1349    permutation [ 8, 7, 1, 6, 2, 5, 4, 3 ]

Algebra 890

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 8 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 6, 2 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 6, 2, 8, 1 ] 
[ 3, 5, 2 ] 
[ 5, 2, 3 ] 
[ 2, 8, 1, 6 ] 
[ 1, 6, 2, 8 ] 
[ 5, 2, 8 ] 
[ 8, 1, 6, 2 ] - [ 8, 5, 2 ] 
[ 2, 3, 5 ] - [ 2, 8, 5 ] 

Cartan matrix

(1 1 1 0 0 1 1 0)
(1 1 1 0 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 1 0 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(0 1 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  3 -> Algebra  690    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  814    permutation [ 8, 6, 1, 7, 2, 5, 4, 3 ]
vertex  5 -> Algebra 1389    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1290    permutation [ 8, 2, 1, 7, 6, 5, 4, 3 ]
vertex  7 -> Algebra 1349    permutation [ 8, 7, 1, 6, 2, 5, 4, 3 ]
vertex  8 -> Algebra  380    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 891

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 6 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 8 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 6, 8, 2 ] 
[ 5, 8, 3 ] 
[ 6, 8, 3 ] 
[ 8, 3, 5 ] 
[ 2, 1, 7 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 6 ] - [ 8, 3, 6 ] 
[ 2, 1, 8 ] - [ 2, 6, 8 ] 
[ 3, 5, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 1)
(1 1 0 0 0 1 0 1)
(0 0 1 0 1 1 0 1)
(0 1 0 1 1 0 0 1)
(0 1 0 0 1 0 0 1)
(0 0 0 0 0 1 0 1)
(0 1 0 0 0 1 1 0)
(0 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1417    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  896    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra  918    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  888    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  8 -> Algebra 1000    permutation [ 6, 8, 1, 7, 2, 5, 4, 3 ]

Algebra 896

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 6 ], [ 4, 5 ], [ 5, 6 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 6, 8, 2 ] 
[ 6, 8, 2, 3 ] 
[ 8, 2, 3, 6 ] 
[ 2, 1, 7 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 6, 8 ] 

Cartan matrix

(1 1 1 0 0 0 1 1)
(1 1 1 0 0 1 0 1)
(0 0 1 0 0 1 0 1)
(0 1 0 1 1 1 0 1)
(0 1 0 0 1 1 0 1)
(0 1 0 0 0 1 0 1)
(0 1 1 0 0 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1420    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  691    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  921    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  891    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra 1195    permutation [ 3, 1, 8, 7, 6, 4, 5, 2 ]
vertex  8 -> Algebra  995    permutation [ 3, 6, 1, 7, 2, 5, 4, 8 ]

Algebra 911

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 2, 3, 8, 5, 1 ] 
[ 3, 8, 5, 1, 2 ] 
[ 8, 5, 1, 2, 3 ] 
[ 1, 2, 3, 8, 5 ] 
[ 5, 1, 2, 3, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(0 1 1 1 1 1 1 1)
(1 0 1 1 1 1 1 1)
(0 0 0 1 0 0 0 0)
(1 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  3 -> Algebra  704    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  954    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1399    permutation [ 1, 3, 2, 7, 4, 8, 5, 6 ]
vertex  7 -> Algebra 1424    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 915

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 2, 3, 4, 8, 1 ] 
[ 3, 4, 8, 1, 2 ] 
[ 4, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 4 ] 
[ 1, 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(0 1 1 1 1 0 0 1)
(1 0 1 1 1 0 0 1)
(1 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(1 1 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  401    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  816    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  887    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1424    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]
vertex  7 -> Algebra 1427    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 916

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 7, 6, 1 ] 
[ 8, 2, 6, 1 ] 
[ 3, 4, 8, 2 ] 
[ 6, 1, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 6, 1, 7 ] 
[ 1, 7, 6 ] - [ 1, 8, 2, 6 ] 
[ 2, 3, 4, 8 ] - [ 2, 6, 1, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 1)
(1 1 1 1 1 1 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(1 0 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1429    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  918    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra  707    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  817    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  888    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  401    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  801    permutation [ 8, 2, 1, 7, 6, 4, 5, 3 ]

Algebra 917

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 6, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 1, 6 ] 
[ 1, 6, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 0 1 0 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 1 1 1 1 1 0 0)
(0 1 1 1 1 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1427    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  708    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  818    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  889    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  401    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  851    permutation [ 8, 7, 1, 6, 2, 4, 5, 3 ]

Algebra 918

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 3, 6 ], [ 4, 5 ], [ 4, 8 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 6, 8, 2 ] 
[ 4, 8, 3 ] 
[ 6, 8, 3 ] 
[ 8, 3, 4 ] 
[ 2, 1, 7 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 6 ] - [ 8, 3, 6 ] 
[ 2, 1, 8 ] - [ 2, 6, 8 ] 
[ 3, 4, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 1)
(1 1 0 0 0 1 0 1)
(0 0 1 1 1 1 0 1)
(0 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 0 1 0 1)
(0 1 0 0 0 1 1 0)
(0 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1430    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  921    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra  820    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  891    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  916    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  8 -> Algebra  495    permutation [ 6, 8, 1, 7, 2, 4, 5, 3 ]

Algebra 921

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 6 ], [ 4, 5 ], [ 4, 6 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 6, 8, 2 ] 
[ 6, 8, 2, 3 ] 
[ 8, 2, 3, 6 ] 
[ 2, 1, 7 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 6, 8 ] 

Cartan matrix

(1 1 1 0 0 0 1 1)
(1 1 1 0 0 1 0 1)
(0 0 1 0 0 1 0 1)
(0 1 0 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(0 1 0 0 0 1 0 1)
(0 1 1 0 0 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1431    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  710    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  927    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra  896    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  918    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra 1014    permutation [ 3, 6, 1, 2, 7, 4, 5, 8 ]
vertex  8 -> Algebra  492    permutation [ 3, 6, 1, 7, 2, 4, 5, 8 ]

Algebra 927

Quiver

[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 7, 2 ], [ 8, 2 ]

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 1, 7 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 2, 1, 8 ] - [ 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 0 0 1 1)
(1 1 1 1 0 1 0 1)
(0 0 1 1 0 1 0 1)
(0 1 0 1 0 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 1 1 1 0 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1432    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  716    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  827    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  653    permutation [ 3, 1, 2, 8, 4, 6, 5, 7 ]
vertex  6 -> Algebra  921    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra  685    permutation [ 3, 1, 8, 7, 4, 6, 5, 2 ]
vertex  8 -> Algebra  735    permutation [ 3, 1, 7, 2, 4, 6, 5, 8 ]

Algebra 947

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ]

Relations

[ 2, 3, 8, 4, 1 ] 
[ 3, 8, 4, 1, 2 ] 
[ 8, 4, 1, 2, 3 ] 
[ 1, 2, 3, 8, 4 ] 
[ 4, 1, 2, 3, 8 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(0 1 1 1 1 1 0 1)
(1 0 1 1 1 1 0 1)
(1 1 1 1 1 1 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  4 -> Algebra 1360    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]
vertex  6 -> Algebra  852    permutation [ 4, 1, 2, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  435    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 951

Quiver

[ 1, 2 ], [ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 2, 3, 8, 1 ] 
[ 4, 8, 1 ] 
[ 3, 8, 1, 2 ] 
[ 8, 1, 2, 3 ] 
[ 4, 8, 5 ] 
[ 5, 4, 8 ] 
[ 8, 1, 4 ] - [ 8, 5, 4 ] 
[ 1, 2, 3, 8 ] - [ 1, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(0 1 1 0 1 1 1 1)
(1 0 1 1 1 1 1 1)
(0 0 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  952    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  3 -> Algebra  736    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  435    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1360    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]

Algebra 952

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 3, 8 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 4, 8, 5, 1 ] 
[ 3, 8, 2 ] 
[ 4, 8, 2 ] 
[ 8, 2, 3 ] 
[ 1, 4, 8, 5 ] 
[ 5, 1, 4, 8 ] 
[ 8, 2, 4 ] - [ 8, 5, 1, 4 ] 
[ 2, 3, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 0 0 1 0 0 0 1)
(0 1 1 1 1 1 1 1)
(1 0 1 0 1 1 1 1)
(0 0 0 1 1 1 1 1)
(1 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra  954    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  737    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  951    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1380    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]

Algebra 953

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 6, 5, 1 ] 
[ 3, 8, 2 ] 
[ 4, 5, 8, 2 ] 
[ 8, 2, 3 ] 
[ 5, 8, 2, 4 ] 
[ 1, 6, 5 ] 
[ 6, 5, 8 ] 
[ 8, 2, 4, 5 ] - [ 8, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 
[ 2, 3, 8 ] - [ 2, 4, 5, 8 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 1 1 1 1 1 1)
(0 0 1 0 0 1 1 1)
(1 0 0 1 1 1 1 1)
(1 1 0 0 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  7 -> Algebra 1047    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1445    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 954

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 2, 4, 8, 5, 1 ] 
[ 4, 8, 5, 1, 2 ] 
[ 8, 5, 1, 2, 4 ] 
[ 1, 2, 4, 8, 5 ] 
[ 5, 1, 2, 4, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 1)
(0 1 0 1 1 1 1 1)
(1 0 1 1 1 1 1 1)
(1 0 0 1 1 1 1 1)
(1 1 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  3 -> Algebra  911    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  952    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1409    permutation [ 1, 3, 2, 7, 4, 8, 5, 6 ]
vertex  7 -> Algebra 1410    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]

Algebra 995

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 5, 1 ] 
[ 4, 5, 8, 3 ] 
[ 5, 8, 3, 4 ] 
[ 1, 2, 5 ] 
[ 2, 5, 8 ] 
[ 3, 4, 5, 8 ] 
[ 5, 1, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 3, 4, 5 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 0 0 0)
(1 0 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(1 1 1 0 1 0 0 1)
(0 1 0 0 1 1 0 0)
(0 1 0 0 1 1 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1208    permutation [ 3, 1, 5, 7, 6, 2, 4, 8 ]
vertex  2 -> Algebra  494    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1013    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  492    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  896    permutation [ 3, 5, 1, 7, 6, 2, 4, 8 ]

Algebra 1000

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 6, 5, 2 ] 
[ 4, 5, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 2, 3, 4 ] 
[ 5, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 4, 5, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 0 0)
(1 1 1 1 1 0 0 1)
(1 1 0 1 1 0 0 0)
(1 1 1 0 1 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  800    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  891    permutation [ 3, 5, 8, 7, 6, 1, 4, 2 ]
vertex  6 -> Algebra 1454    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  495    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  494    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1013

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 4, 1 ] 
[ 1, 2, 4 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 1 0 0 0)
(1 0 1 1 0 0 0 0)
(1 1 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 1 0 1 1 1 0 0)
(0 1 0 1 1 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1309    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  505    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  995    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  503    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1195    permutation [ 1, 3, 8, 5, 2, 7, 6, 4 ]

Algebra 1014

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 1 ], [ 4, 5 ], [ 5, 3 ], [ 6, 2 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 2, 8, 4, 1 ] 
[ 8, 4, 1, 2 ] 
[ 8, 4, 5, 3 ] 
[ 1, 2, 8, 4 ] 
[ 5, 3, 8, 4 ] 
[ 3, 8, 4, 5 ] 
[ 4, 1, 2, 8 ] - [ 4, 5, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 1 1 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 1 0 1 0 0 1)
(0 1 0 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1229    permutation [ 3, 1, 4, 6, 7, 2, 5, 8 ]
vertex  3 -> Algebra 1377    permutation [ 1, 8, 3, 5, 2, 6, 7, 4 ]
vertex  4 -> Algebra  684    permutation [ 1, 3, 8, 5, 2, 6, 7, 4 ]
vertex  5 -> Algebra  921    permutation [ 3, 4, 1, 6, 7, 2, 5, 8 ]
vertex  6 -> Algebra  685    permutation [ 1, 3, 8, 5, 2, 6, 7, 4 ]
vertex  7 -> Algebra 1195    permutation [ 1, 3, 8, 5, 2, 7, 6, 4 ]
vertex  8 -> Algebra  503    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1015

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 1 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 6, 1 ] 
[ 5, 3, 4 ] 
[ 6, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 2, 6 ] 
[ 2, 6, 8 ] 
[ 3, 4, 6, 8 ] 
[ 6, 1, 2 ] - [ 6, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 6, 8, 3 ] 
[ 8, 2, 6 ] - [ 8, 3, 4, 6 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 1 0 0)
(1 0 1 1 0 1 0 0)
(1 1 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(1 1 1 0 0 1 0 1)
(0 1 0 0 0 1 1 0)
(0 1 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1314    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  504    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1022    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  6 -> Algebra  703    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  7 -> Algebra  705    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1462    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1022

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 4, 1 ] 
[ 1, 2, 4 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 4, 6, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 0 1 0 0)
(1 0 1 1 0 0 0 0)
(1 1 1 1 0 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 1 0 1 0 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1324    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  507    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1031    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra 1015    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra  696    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1204    permutation [ 1, 3, 8, 5, 6, 2, 7, 4 ]

Algebra 1031

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 4, 1 ] 
[ 1, 2, 4 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 1 1 0 0)
(1 0 1 1 0 0 0 0)
(1 1 1 1 1 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 1 0 1 1 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1336    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  513    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1022    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  715    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1226    permutation [ 1, 3, 8, 5, 6, 2, 7, 4 ]

Algebra 1047

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 6 ], [ 6, 1 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 6, 1 ] 
[ 4, 8, 3 ] 
[ 5, 6, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 8, 3, 5 ] 
[ 1, 2, 6 ] 
[ 2, 6, 8 ] 
[ 6, 1, 2 ] - [ 6, 8, 2 ] 
[ 8, 2, 6 ] - [ 8, 3, 5, 6 ] 
[ 3, 4, 8 ] - [ 3, 5, 6, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 1 0 0)
(1 1 1 1 1 1 0 1)
(0 1 0 1 0 0 0 1)
(1 1 0 0 1 1 0 1)
(1 1 1 0 0 1 0 1)
(0 1 0 0 0 1 1 0)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  2 -> Algebra  528    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  953    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1471    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1049

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 7 ], [ 3, 5 ], [ 3, 8 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 7, 6, 2 ] 
[ 5, 6, 2, 3 ] 
[ 8, 2, 3 ] 
[ 6, 2, 3, 5 ] 
[ 6, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 5, 6, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 5, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 1 0)
(1 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(1 1 0 0 1 1 0 0)
(1 1 1 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra  872    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1472    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1453    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  7 -> Algebra 1189    permutation [ 2, 6, 7, 5, 1, 8, 4, 3 ]
vertex  8 -> Algebra  528    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1163

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 5, 4, 2, 3, 1 ] 
[ 3, 1, 5, 4, 2 ] 
[ 1, 5, 4, 2, 3 ] 
[ 2, 3, 1, 5, 4 ] 
[ 4, 2, 3, 1, 5 ] 

Cartan matrix

(1 1 0 1 1 1 1 0)
(1 1 1 0 1 1 1 0)
(1 0 1 1 1 1 1 0)
(1 1 1 1 0 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra  653    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1336    permutation [ 2, 3, 5, 1, 6, 7, 8, 4 ]
vertex  7 -> Algebra 1432    permutation [ 2, 3, 1, 5, 7, 6, 8, 4 ]
vertex  8 -> Algebra  791    permutation [ 1, 4, 3, 8, 5, 6, 7, 2 ]

Algebra 1170

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 6 ], [ 4, 7 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 7, 1 ] 
[ 6, 3, 4 ] 
[ 7, 1, 8, 3, 4 ] 
[ 3, 4, 6 ] 
[ 1, 8, 3, 4, 7 ] 
[ 3, 4, 7, 1, 8 ] 
[ 4, 6, 3 ] - [ 4, 7, 1, 8, 3 ] 

Cartan matrix

(1 0 1 1 0 0 0 1)
(1 1 1 1 0 0 1 0)
(1 0 1 1 0 0 1 0)
(1 0 1 1 0 1 1 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(1 0 1 0 0 0 1 1)
(0 0 1 1 0 0 1 1)

Good mutations

vertex  2 -> Algebra 1260    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1197    permutation [ 2, 1, 8, 7, 3, 6, 5, 4 ]
vertex  5 -> Algebra 1175    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  658    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1287    permutation [ 2, 3, 6, 4, 7, 1, 8, 5 ]

Algebra 1175

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 7 ], [ 5, 3 ], [ 5, 6 ], [ 7, 1 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 7, 1 ] 
[ 5, 3, 4 ] 
[ 7, 1, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 8, 3, 4, 7 ] 
[ 3, 4, 7, 1, 8 ] 
[ 4, 5, 3 ] - [ 4, 7, 1, 8, 3 ] 

Cartan matrix

(1 0 1 1 0 0 0 1)
(1 1 1 1 0 0 1 0)
(1 0 1 1 0 0 1 0)
(1 0 1 1 1 1 1 1)
(0 0 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(1 0 1 0 0 0 1 1)
(0 0 1 1 0 0 1 1)

Good mutations

vertex  2 -> Algebra 1189    permutation [ 3, 1, 8, 7, 2, 5, 6, 4 ]
vertex  3 -> Algebra  686    permutation [ 2, 1, 8, 7, 3, 5, 6, 4 ]
vertex  6 -> Algebra 1170    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  664    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  872    permutation [ 2, 3, 4, 6, 7, 1, 8, 5 ]

Algebra 1188

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 3 ], [ 3, 5 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 6, 5 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 6, 5, 1 ] 
[ 3, 8, 4, 2 ] 
[ 5, 1, 3 ] 
[ 2, 3, 8, 4 ] 
[ 5, 1, 6 ] 
[ 1, 3, 8 ] 
[ 4, 2, 3, 8 ] 
[ 3, 5, 1 ] - [ 3, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 4, 2, 3 ] 
[ 1, 3, 5 ] - [ 1, 6, 5 ] 

Cartan matrix

(1 0 1 0 1 1 0 0)
(1 1 1 0 1 0 0 1)
(1 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 0)
(1 0 0 0 1 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1260    permutation [ 2, 1, 5, 8, 7, 6, 4, 3 ]
vertex  2 -> Algebra 1367    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1462    permutation [ 1, 6, 2, 8, 4, 3, 7, 5 ]
vertex  4 -> Algebra  827    permutation [ 2, 8, 5, 1, 7, 6, 4, 3 ]
vertex  5 -> Algebra  685    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  680    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  679    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1189

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 6, 1 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 3, 1, 8, 4, 2 ] 
[ 1, 8, 4, 2, 3 ] 
[ 2, 3, 1, 8, 4 ] 
[ 1, 8, 6 ] 
[ 4, 2, 3, 1, 8 ] 
[ 6, 1, 8 ] 
[ 8, 4, 2, 3, 1 ] - [ 8, 6, 1 ] 

Cartan matrix

(1 1 0 1 1 0 0 1)
(1 1 1 0 1 0 0 1)
(1 0 1 1 1 0 0 1)
(1 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  680    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1049    permutation [ 5, 1, 8, 7, 4, 2, 3, 6 ]
vertex  4 -> Algebra  770    permutation [ 2, 1, 5, 8, 6, 7, 4, 3 ]
vertex  5 -> Algebra 1175    permutation [ 2, 5, 1, 8, 6, 7, 4, 3 ]
vertex  7 -> Algebra 1260    permutation [ 2, 1, 5, 8, 7, 6, 4, 3 ]

Algebra 1190

Quiver

[ 1, 6 ], [ 2, 5 ], [ 2, 8 ], [ 3, 1 ], [ 3, 2 ], [ 4, 2 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 6, 5, 3, 1 ] 
[ 5, 3, 2 ] 
[ 1, 6, 5, 3 ] 
[ 2, 8, 4 ] 
[ 5, 3, 1, 6 ] 
[ 3, 2, 8 ] 
[ 4, 2, 8 ] 
[ 8, 3, 2 ] - [ 8, 4, 2 ] 
[ 2, 5, 3 ] - [ 2, 8, 3 ] 
[ 3, 1, 6, 5 ] - [ 3, 2, 5 ] 

Cartan matrix

(1 0 0 0 1 1 1 0)
(1 1 1 0 1 0 0 1)
(1 1 1 0 1 1 1 0)
(0 1 0 1 1 0 0 0)
(1 0 1 0 1 0 0 0)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1472    permutation [ 5, 3, 8, 7, 4, 2, 1, 6 ]
vertex  2 -> Algebra 1506    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  680    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  705    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1505    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1462    permutation [ 1, 6, 2, 8, 4, 3, 7, 5 ]
vertex  8 -> Algebra  690    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1195

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 1 ] 
[ 3, 8, 4, 2 ] 
[ 2, 3, 8, 4 ] 
[ 3, 8, 1, 5 ] 
[ 1, 5, 3, 8 ] 
[ 4, 2, 3, 8 ] 
[ 8, 1, 5, 3 ] - [ 8, 4, 2, 3 ] 

Cartan matrix

(1 0 1 0 1 0 0 0)
(1 1 1 0 0 0 0 1)
(1 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 1 1 1 0 1 1)
(1 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1207    permutation [ 2, 1, 8, 6, 7, 5, 4, 3 ]
vertex  2 -> Algebra 1374    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1013    permutation [ 1, 5, 2, 8, 4, 7, 6, 3 ]
vertex  4 -> Algebra  896    permutation [ 2, 8, 1, 6, 7, 5, 4, 3 ]
vertex  6 -> Algebra 1014    permutation [ 1, 5, 2, 8, 4, 7, 6, 3 ]
vertex  8 -> Algebra  682    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1197

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 8, 5, 1 ] 
[ 3, 8, 4, 2 ] 
[ 2, 3, 8, 4 ] 
[ 1, 8, 5 ] 
[ 3, 8, 5 ] 
[ 4, 2, 3, 8 ] 
[ 8, 4, 2, 3 ] - [ 8, 5, 3 ] 
[ 5, 1, 8 ] - [ 5, 3, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 0)
(1 0 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  685    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1217    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  716    permutation [ 2, 1, 8, 5, 7, 6, 4, 3 ]
vertex  5 -> Algebra 1170    permutation [ 2, 1, 5, 8, 7, 6, 4, 3 ]
vertex  6 -> Algebra 1229    permutation [ 2, 1, 8, 6, 7, 5, 4, 3 ]
vertex  7 -> Algebra  686    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1202

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 3 ], [ 3, 6 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 7, 6, 1 ] 
[ 3, 8, 5, 2 ] 
[ 6, 1, 3 ] 
[ 2, 3, 8, 5 ] 
[ 6, 1, 7 ] 
[ 1, 3, 8 ] 
[ 5, 2, 3, 8 ] 
[ 3, 6, 1 ] - [ 3, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 5, 2, 3 ] 
[ 1, 3, 6 ] - [ 1, 7, 6 ] 

Cartan matrix

(1 0 1 0 0 1 1 0)
(1 1 1 0 0 1 0 1)
(1 0 1 0 1 1 0 1)
(0 1 1 1 1 1 0 0)
(0 1 1 0 1 1 0 0)
(1 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1509    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1290    permutation [ 8, 3, 1, 7, 6, 5, 4, 2 ]
vertex  3 -> Algebra  794    permutation [ 8, 2, 1, 7, 6, 5, 4, 3 ]
vertex  4 -> Algebra  795    permutation [ 8, 2, 1, 7, 6, 5, 4, 3 ]
vertex  5 -> Algebra 1505    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra  690    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  688    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1204

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 3 ], [ 7, 6 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 6, 3, 8, 1 ] 
[ 3, 8, 5, 2 ] 
[ 2, 3, 8, 5 ] 
[ 3, 8, 1, 6 ] 
[ 1, 6, 3, 8 ] 
[ 5, 2, 3, 8 ] 
[ 8, 1, 6, 3 ] - [ 8, 5, 2, 3 ] 

Cartan matrix

(1 0 1 0 0 1 0 0)
(1 1 1 0 0 0 0 1)
(1 0 1 0 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 0 1 0 1 1 0 1)
(0 0 1 0 1 1 1 1)
(1 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1510    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1349    permutation [ 8, 7, 1, 6, 3, 5, 4, 2 ]
vertex  3 -> Algebra 1022    permutation [ 1, 6, 2, 8, 4, 5, 7, 3 ]
vertex  4 -> Algebra 1226    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1462    permutation [ 1, 6, 2, 5, 4, 8, 7, 3 ]
vertex  7 -> Algebra  690    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  689    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1205

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 1 ], [ 6, 3 ], [ 6, 7 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 8, 6, 1 ] 
[ 3, 8, 5, 2 ] 
[ 2, 3, 8, 5 ] 
[ 1, 8, 6 ] 
[ 3, 8, 6 ] 
[ 5, 2, 3, 8 ] 
[ 8, 5, 2, 3 ] - [ 8, 6, 3 ] 
[ 6, 1, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 0 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 1 1 0 1 0 0 0)
(1 0 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  690    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1211    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1227    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1472    permutation [ 3, 8, 5, 7, 4, 2, 1, 6 ]
vertex  6 -> Algebra 1511    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1510    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1207

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 6 ], [ 3, 7 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 6, 8 ], [ 7, 1 ], [ 8, 3 ]

Relations

[ 8, 3, 7, 1 ] 
[ 3, 6, 2 ] 
[ 7, 1, 8, 3 ] 
[ 2, 3, 6 ] 
[ 8, 3, 6 ] 
[ 1, 8, 3, 7 ] 
[ 6, 2, 3 ] - [ 6, 8, 3 ] 
[ 3, 6, 8 ] - [ 3, 7, 1, 8 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(1 1 1 0 0 0 1 0)
(1 0 1 0 0 1 1 1)
(0 1 1 1 1 1 1 1)
(0 1 1 0 1 1 1 1)
(0 1 1 0 0 1 1 1)
(1 0 0 0 0 0 1 1)
(0 0 1 0 0 0 1 1)

Good mutations

vertex  2 -> Algebra 1195    permutation [ 2, 1, 8, 7, 6, 4, 5, 3 ]
vertex  4 -> Algebra 1229    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  691    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1309    permutation [ 6, 2, 1, 3, 7, 5, 4, 8 ]

Algebra 1208

Quiver

[ 1, 7 ], [ 2, 3 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 7, 3 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 7, 3, 8, 1 ] 
[ 3, 8, 6, 2 ] 
[ 2, 3, 8, 6 ] 
[ 3, 8, 1, 7 ] 
[ 1, 7, 3, 8 ] 
[ 6, 2, 3, 8 ] 
[ 8, 1, 7, 3 ] - [ 8, 6, 2, 3 ] 

Cartan matrix

(1 0 1 0 0 0 1 0)
(1 1 1 0 0 0 0 1)
(1 0 1 0 0 1 0 1)
(0 1 1 1 1 1 0 0)
(0 1 1 0 1 1 0 0)
(0 1 1 0 0 1 0 0)
(0 0 1 0 0 1 1 1)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1381    permutation [ 6, 2, 7, 1, 3, 5, 4, 8 ]
vertex  2 -> Algebra  995    permutation [ 2, 6, 1, 7, 3, 5, 4, 8 ]
vertex  3 -> Algebra 1210    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  792    permutation [ 6, 2, 1, 7, 3, 5, 4, 8 ]
vertex  6 -> Algebra  794    permutation [ 6, 2, 1, 7, 3, 5, 4, 8 ]
vertex  7 -> Algebra 1309    permutation [ 6, 2, 1, 3, 7, 5, 4, 8 ]
vertex  8 -> Algebra  691    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1210

Quiver

[ 1, 7 ], [ 2, 3 ], [ 3, 1 ], [ 3, 6 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 7, 3 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 7, 3, 1 ] 
[ 1, 7, 3 ] 
[ 6, 2, 3 ] 
[ 2, 3, 6 ] 
[ 2, 3, 8 ] 
[ 7, 3, 8 ] 
[ 3, 6, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 7, 3 ] 
[ 3, 1, 7 ] - [ 3, 8, 7 ] 

Cartan matrix

(1 0 0 0 0 0 1 0)
(1 1 1 0 0 0 0 0)
(1 1 1 0 0 1 1 1)
(0 1 0 1 1 1 0 0)
(0 1 0 0 1 1 0 0)
(0 1 0 0 0 1 0 0)
(0 0 1 0 0 1 1 0)
(0 1 1 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1361    permutation [ 6, 8, 7, 1, 2, 5, 4, 3 ]
vertex  4 -> Algebra  783    permutation [ 6, 8, 1, 7, 2, 5, 4, 3 ]
vertex  6 -> Algebra  785    permutation [ 6, 8, 1, 7, 2, 5, 4, 3 ]
vertex  8 -> Algebra 1208    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 1211

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 5 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 1 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 3, 8, 6, 1 ] 
[ 5, 2, 3 ] 
[ 2, 3, 5 ] 
[ 1, 3, 8, 6 ] 
[ 2, 3, 8 ] 
[ 6, 1, 3, 8 ] 
[ 3, 5, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 6, 1, 3 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(0 1 1 0 0 0 0 0)
(0 1 1 0 1 1 1 1)
(0 1 0 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(1 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  696    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1277    permutation [ 3, 8, 1, 7, 2, 5, 4, 6 ]
vertex  4 -> Algebra 1231    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1219    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra 1367    permutation [ 3, 8, 7, 6, 2, 5, 4, 1 ]
vertex  7 -> Algebra 1324    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1205    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 1217

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 3, 8, 5, 1 ] 
[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 1, 3, 8, 5 ] 
[ 2, 3, 8 ] 
[ 5, 1, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 5, 1, 3 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 1 1 1 1 1 0 1)
(0 1 0 1 0 0 0 0)
(1 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  703    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1424    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1233    permutation [ 2, 1, 3, 5, 7, 6, 4, 8 ]
vertex  5 -> Algebra 1310    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  6 -> Algebra  816    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  704    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1197    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 1218

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 3, 8, 1 ] 
[ 5, 8, 1 ] 
[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 5, 8, 6 ] 
[ 2, 3, 8 ] 
[ 6, 5, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 1, 3 ] - [ 8, 2, 3 ] 
[ 8, 1, 5 ] - [ 8, 6, 5 ] 
[ 1, 3, 8 ] - [ 1, 5, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(0 1 1 0 0 0 0 0)
(0 1 1 1 0 1 1 1)
(0 1 0 1 0 0 0 0)
(0 1 0 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1219    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  2 -> Algebra 1399    permutation [ 1, 2, 3, 7, 4, 8, 5, 6 ]
vertex  5 -> Algebra  704    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1310    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra  872    permutation [ 1, 8, 3, 7, 4, 2, 5, 6 ]

Algebra 1219

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 5, 8, 6, 1 ] 
[ 4, 2, 3 ] 
[ 5, 8, 2, 3 ] 
[ 2, 3, 4 ] 
[ 1, 5, 8, 6 ] 
[ 2, 3, 5, 8 ] 
[ 6, 1, 5, 8 ] 
[ 3, 4, 2 ] - [ 3, 5, 8, 2 ] 
[ 8, 2, 3, 5 ] - [ 8, 6, 1, 5 ] 

Cartan matrix

(1 1 0 0 1 0 0 1)
(0 1 1 0 1 0 0 0)
(0 1 1 1 1 1 1 1)
(0 1 0 1 0 0 0 0)
(0 1 0 0 1 1 1 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  705    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1425    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1211    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra 1218    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  7 -> Algebra 1314    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1472    permutation [ 8, 5, 3, 7, 4, 2, 1, 6 ]

Algebra 1226

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 3 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 6, 3, 8, 1 ] 
[ 3, 8, 4, 2 ] 
[ 2, 3, 8, 4 ] 
[ 3, 8, 1, 6 ] 
[ 1, 6, 3, 8 ] 
[ 4, 2, 3, 8 ] 
[ 8, 1, 6, 3 ] - [ 8, 4, 2, 3 ] 

Cartan matrix

(1 0 1 0 0 1 0 0)
(1 1 1 0 0 0 0 1)
(1 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 0 1)
(0 0 1 1 1 1 1 1)
(1 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1518    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  851    permutation [ 8, 7, 1, 6, 3, 4, 5, 2 ]
vertex  3 -> Algebra 1031    permutation [ 1, 6, 2, 8, 4, 5, 7, 3 ]
vertex  5 -> Algebra 1204    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  709    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  708    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1227

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 1 ], [ 6, 3 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 8, 6, 1 ] 
[ 3, 8, 4, 2 ] 
[ 2, 3, 8, 4 ] 
[ 1, 8, 6 ] 
[ 3, 8, 6 ] 
[ 4, 2, 3, 8 ] 
[ 8, 4, 2, 3 ] - [ 8, 6, 3 ] 
[ 6, 1, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 1 1 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 0 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  709    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1231    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  5 -> Algebra 1205    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1519    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1518    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1229

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 6 ], [ 3, 7 ], [ 4, 5 ], [ 4, 6 ], [ 6, 2 ], [ 6, 8 ], [ 7, 1 ], [ 8, 3 ]

Relations

[ 8, 3, 7, 1 ] 
[ 3, 6, 2 ] 
[ 7, 1, 8, 3 ] 
[ 2, 3, 6 ] 
[ 8, 3, 6 ] 
[ 1, 8, 3, 7 ] 
[ 6, 2, 3 ] - [ 6, 8, 3 ] 
[ 3, 6, 8 ] - [ 3, 7, 1, 8 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(1 1 1 0 0 0 1 0)
(1 0 1 0 0 1 1 1)
(0 1 1 1 1 1 1 1)
(0 0 0 0 1 0 0 0)
(0 1 1 0 0 1 1 1)
(1 0 0 0 0 0 1 1)
(0 0 1 0 0 0 1 1)

Good mutations

vertex  2 -> Algebra 1014    permutation [ 2, 6, 1, 3, 7, 4, 5, 8 ]
vertex  4 -> Algebra 1197    permutation [ 2, 1, 8, 7, 6, 4, 5, 3 ]
vertex  5 -> Algebra 1207    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  710    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  816    permutation [ 6, 2, 1, 3, 7, 4, 5, 8 ]

Algebra 1231

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 1 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 3, 8, 6, 1 ] 
[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 1, 3, 8, 6 ] 
[ 2, 3, 8 ] 
[ 6, 1, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 6, 1, 3 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(0 1 1 0 0 0 0 0)
(0 1 1 1 1 1 1 1)
(0 1 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  715    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  791    permutation [ 3, 8, 1, 7, 2, 4, 5, 6 ]
vertex  5 -> Algebra 1211    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  859    permutation [ 3, 8, 7, 6, 2, 4, 5, 1 ]
vertex  7 -> Algebra 1336    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1227    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 1233

Quiver

[ 1, 7 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 4, 6 ], [ 5, 6 ], [ 7, 3 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 7, 3, 8, 1 ] 
[ 3, 8, 4, 2 ] 
[ 2, 3, 8, 4 ] 
[ 3, 8, 1, 7 ] 
[ 1, 7, 3, 8 ] 
[ 4, 2, 3, 8 ] 
[ 8, 1, 7, 3 ] - [ 8, 4, 2, 3 ] 

Cartan matrix

(1 0 1 0 0 0 1 0)
(1 1 1 0 0 0 0 1)
(1 0 1 1 0 1 0 1)
(0 1 1 1 0 1 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 1 1 1)
(1 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1380    permutation [ 4, 2, 7, 1, 3, 6, 5, 8 ]
vertex  2 -> Algebra  735    permutation [ 2, 1, 7, 3, 4, 6, 5, 8 ]
vertex  3 -> Algebra 1234    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  5 -> Algebra  737    permutation [ 2, 1, 7, 3, 4, 6, 5, 8 ]
vertex  6 -> Algebra  792    permutation [ 4, 2, 1, 7, 3, 6, 5, 8 ]
vertex  7 -> Algebra 1217    permutation [ 2, 1, 3, 7, 4, 6, 5, 8 ]
vertex  8 -> Algebra  716    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1234

Quiver

[ 1, 7 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 4, 6 ], [ 5, 6 ], [ 7, 3 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 7, 3, 1 ] 
[ 1, 7, 3 ] 
[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 2, 3, 8 ] 
[ 7, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 7, 3 ] 
[ 3, 1, 7 ] - [ 3, 8, 7 ] 

Cartan matrix

(1 0 0 0 0 0 1 0)
(1 1 1 0 0 0 0 0)
(1 1 1 1 0 1 1 1)
(0 1 0 1 0 1 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 1 1 0)
(0 1 1 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1360    permutation [ 4, 8, 7, 1, 2, 6, 5, 3 ]
vertex  5 -> Algebra  736    permutation [ 8, 1, 7, 2, 4, 6, 5, 3 ]
vertex  6 -> Algebra  783    permutation [ 4, 8, 1, 7, 2, 6, 5, 3 ]
vertex  8 -> Algebra 1233    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 1260

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 6 ], [ 4, 7 ], [ 5, 6 ], [ 6, 2 ], [ 7, 1 ], [ 8, 2 ]

Relations

[ 8, 2, 4, 7, 1 ] 
[ 6, 2, 4 ] 
[ 7, 1, 8, 2, 4 ] 
[ 2, 4, 6 ] 
[ 1, 8, 2, 4, 7 ] 
[ 2, 4, 7, 1, 8 ] 
[ 4, 6, 2 ] - [ 4, 7, 1, 8, 2 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(1 1 1 1 0 0 1 0)
(0 0 1 0 0 0 0 0)
(1 1 1 1 0 1 1 1)
(0 1 1 0 1 1 0 0)
(0 1 1 0 0 1 0 0)
(1 1 1 0 0 0 1 1)
(0 1 1 1 0 0 1 1)

Good mutations

vertex  2 -> Algebra 1188    permutation [ 2, 1, 8, 7, 3, 6, 5, 4 ]
vertex  3 -> Algebra 1170    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1189    permutation [ 2, 1, 8, 7, 3, 6, 5, 4 ]
vertex  7 -> Algebra  764    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1453    permutation [ 3, 2, 6, 4, 7, 1, 8, 5 ]

Algebra 1277

Quiver

[ 1, 5 ], [ 2, 8 ], [ 3, 1 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 5, 2, 8, 3, 1 ] 
[ 8, 3, 1, 5, 2 ] 
[ 1, 5, 2, 8, 3 ] 
[ 2, 8, 3, 1, 5 ] 
[ 3, 1, 5, 2, 8 ] 

Cartan matrix

(1 1 0 1 1 1 0 1)
(1 1 1 1 0 0 0 1)
(1 1 1 0 1 1 0 0)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 0 1 1 1 1 0 1)

Good mutations

vertex  4 -> Algebra 1432    permutation [ 8, 3, 1, 5, 7, 6, 4, 2 ]
vertex  5 -> Algebra 1211    permutation [ 3, 5, 1, 7, 6, 8, 4, 2 ]
vertex  6 -> Algebra 1426    permutation [ 3, 1, 6, 7, 5, 8, 4, 2 ]
vertex  7 -> Algebra  791    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  864    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1282

Quiver

[ 1, 4 ], [ 1, 6 ], [ 2, 8 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 6, 2 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 4, 3, 1 ] 
[ 6, 2, 8, 3, 1 ] 
[ 8, 3, 1, 6, 2 ] 
[ 3, 1, 4 ] 
[ 2, 8, 3, 1, 6 ] 
[ 3, 1, 6, 2, 8 ] 
[ 1, 4, 3 ] - [ 1, 6, 2, 8, 3 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 1 0 1 0 0 1)
(1 1 1 0 1 1 1 0)
(0 0 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 0 1 0 1 1 1 1)

Good mutations

vertex  3 -> Algebra  795    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1519    permutation [ 5, 2, 8, 6, 7, 3, 4, 1 ]
vertex  7 -> Algebra 1509    permutation [ 3, 2, 8, 7, 6, 5, 4, 1 ]
vertex  8 -> Algebra  869    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1287

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 7 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 2, 4, 3 ] 
[ 3, 2, 4 ] 
[ 5, 6, 2, 4 ] 
[ 6, 2, 4, 5 ] 
[ 6, 2, 7 ] 
[ 4, 3, 2 ] - [ 4, 5, 6, 2 ] 
[ 2, 4, 5, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 1 0 1 1 1 1 0)
(0 1 0 1 1 1 1 0)
(0 1 1 0 0 0 1 0)
(0 1 1 1 1 1 0 0)
(0 1 0 0 1 1 0 0)
(0 1 0 1 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1453    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1310    permutation [ 3, 1, 6, 4, 5, 7, 8, 2 ]
vertex  7 -> Algebra 1170    permutation [ 6, 1, 2, 4, 8, 3, 5, 7 ]
vertex  8 -> Algebra  872    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1289

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 4, 5, 6, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 6, 2, 3, 4 ] 
[ 2, 3, 4, 5, 6 ] 
[ 7, 5, 6 ] 
[ 5, 6, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 5, 6, 2 ] - [ 3, 8, 2 ] 
[ 6, 2, 3, 4, 5 ] - [ 6, 7, 5 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(0 1 1 1 1 0 0 0)
(0 1 1 1 1 1 0 1)
(0 1 0 1 1 1 0 0)
(0 1 1 0 1 1 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 1 0 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1454    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1491    permutation [ 1, 3, 2, 8, 4, 5, 7, 6 ]
vertex  6 -> Algebra  800    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1290

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 6, 2 ], [ 7, 6 ], [ 8, 6 ]

Relations

[ 3, 2, 1 ] 
[ 6, 2, 1 ] 
[ 5, 3, 2 ] 
[ 8, 6, 2 ] 
[ 4, 5, 3 ] 
[ 5, 3, 4 ] 
[ 6, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 6, 2 ] 
[ 2, 1, 3 ] - [ 2, 5, 3 ] 
[ 3, 2, 5 ] - [ 3, 4, 5 ] 
[ 2, 1, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 1 1 1 1 1 0 0)
(1 1 1 0 1 1 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 1 0 1 0 0 0)
(0 1 0 0 1 1 0 0)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  888    permutation [ 3, 2, 8, 7, 6, 5, 4, 1 ]
vertex  2 -> Algebra  800    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  890    permutation [ 3, 2, 8, 7, 6, 5, 4, 1 ]
vertex  6 -> Algebra 1529    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  801    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1202    permutation [ 3, 8, 2, 7, 6, 5, 4, 1 ]

Algebra 1309

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 1 1 0 0 0)
(0 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(1 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(1 1 0 1 1 1 0 0)
(1 1 0 1 1 1 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  818    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1013    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1427    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1208    permutation [ 3, 2, 4, 7, 6, 1, 5, 8 ]
vertex  7 -> Algebra  816    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1207    permutation [ 3, 2, 4, 7, 6, 1, 5, 8 ]

Algebra 1310

Quiver

[ 1, 6 ], [ 2, 4 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 6, 8, 1 ] 
[ 4, 8, 2 ] 
[ 6, 8, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 6, 8 ] 
[ 3, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 8, 1, 6 ] - [ 8, 2, 6 ] 
[ 2, 4, 8 ] - [ 2, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 0)
(0 1 1 1 1 1 0 1)
(0 0 1 1 0 0 0 0)
(1 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 0 1 0 0 1 0 1)
(1 0 0 0 0 1 1 0)
(1 1 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra  817    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1314    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1429    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1217    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  7 -> Algebra 1218    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1287    permutation [ 2, 8, 1, 4, 5, 3, 6, 7 ]

Algebra 1314

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 6, 8, 1 ] 
[ 6, 8, 1, 2 ] 
[ 5, 3, 4 ] 
[ 6, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 2, 6, 8 ] 
[ 3, 4, 6, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 8, 3 ] 
[ 8, 1, 2, 6 ] - [ 8, 3, 4, 6 ] 

Cartan matrix

(1 1 0 0 0 1 0 0)
(0 1 1 0 0 1 0 1)
(0 0 1 1 0 1 0 0)
(1 0 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(1 0 1 0 0 1 0 1)
(1 1 0 0 0 1 1 0)
(1 1 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra  820    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1015    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1430    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1324    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  6 -> Algebra 1310    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  7 -> Algebra 1219    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1536    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1324

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 1, 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 6, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 1 0 1 0 0)
(0 1 1 1 0 1 0 1)
(0 0 1 1 0 0 0 0)
(1 0 1 1 0 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(1 1 0 1 0 1 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  827    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1022    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1432    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1336    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra 1314    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra 1211    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1510    permutation [ 2, 3, 8, 5, 6, 1, 7, 4 ]

Algebra 1336

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 1 1 1 0 0)
(0 1 1 1 1 1 0 1)
(0 0 1 1 0 0 0 0)
(1 0 1 1 1 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(1 1 0 1 1 1 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  837    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1031    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1163    permutation [ 4, 1, 2, 8, 3, 5, 6, 7 ]
vertex  6 -> Algebra 1324    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1231    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1518    permutation [ 2, 3, 8, 5, 6, 1, 7, 4 ]

Algebra 1349

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 7, 6 ], [ 8, 6 ]

Relations

[ 3, 4, 5, 1 ] 
[ 6, 5, 1 ] 
[ 4, 5, 1, 3 ] 
[ 5, 1, 3, 4 ] 
[ 8, 6, 5 ] 
[ 6, 5, 8 ] 
[ 1, 3, 4, 5 ] - [ 1, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 0 1 1 1 1 0 0)
(1 1 0 1 1 1 0 1)
(0 0 1 1 1 0 0 1)
(1 0 0 1 1 1 0 1)
(1 0 1 0 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  889    permutation [ 3, 5, 8, 7, 6, 4, 2, 1 ]
vertex  2 -> Algebra  890    permutation [ 3, 5, 8, 7, 6, 4, 2, 1 ]
vertex  6 -> Algebra 1484    permutation [ 1, 3, 2, 8, 4, 5, 7, 6 ]
vertex  7 -> Algebra  851    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1204    permutation [ 3, 8, 5, 7, 6, 4, 2, 1 ]

Algebra 1354

Quiver

[ 1, 2 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 6, 5 ], [ 7, 6 ], [ 8, 1 ]

Relations

[ 2, 3, 4, 8, 1 ] 
[ 3, 4, 8, 1, 2 ] 
[ 4, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 4 ] 
[ 1, 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(0 1 1 1 0 0 0 1)
(1 0 1 1 1 0 0 1)
(1 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1361    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  5 -> Algebra  854    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  852    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1356

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 6, 7 ], [ 7, 5 ], [ 8, 1 ]

Relations

[ 2, 3, 4, 8, 1 ] 
[ 3, 4, 8, 1, 2 ] 
[ 4, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 4 ] 
[ 1, 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 0 0 0 1)
(1 1 1 1 1 0 0 0)
(1 1 1 1 1 1 1 0)
(1 1 1 1 1 0 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  861    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1358    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1358

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 2, 3, 4, 8, 1 ] 
[ 3, 4, 8, 1, 2 ] 
[ 4, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 4 ] 
[ 1, 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 0 0 0 1)
(1 1 1 1 1 0 0 0)
(1 1 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  863    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  854    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1356    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1360

Quiver

[ 1, 5 ], [ 1, 6 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 8 ], [ 7, 6 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 5, 8, 1 ] 
[ 3, 4, 8, 2 ] 
[ 5, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 1, 5, 8 ] 
[ 8, 1, 5 ] - [ 8, 2, 5 ] 
[ 2, 3, 4, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 1 1 0 0)
(0 1 1 1 1 0 0 1)
(1 0 1 1 0 1 0 1)
(1 1 0 1 1 1 0 1)
(0 0 0 0 1 0 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1380    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  4 -> Algebra 1234    permutation [ 4, 5, 8, 1, 7, 6, 3, 2 ]
vertex  5 -> Algebra  947    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]
vertex  6 -> Algebra  856    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  951    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]

Algebra 1361

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 5, 8, 1 ] 
[ 3, 4, 8, 2 ] 
[ 5, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 1, 5, 8 ] 
[ 8, 1, 5 ] - [ 8, 2, 5 ] 
[ 2, 3, 4, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 1 0 0 0)
(0 1 1 1 1 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 1)
(1 0 0 0 1 1 0 0)
(1 0 0 0 1 1 1 0)
(1 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  858    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1381    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  4 -> Algebra 1210    permutation [ 4, 5, 8, 7, 6, 1, 3, 2 ]
vertex  5 -> Algebra 1354    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  7 -> Algebra  856    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1367

Quiver

[ 1, 2 ], [ 1, 6 ], [ 2, 3 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 1 ], [ 6, 5 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 6, 5, 1 ] 
[ 3, 4, 2 ] 
[ 5, 1, 2 ] 
[ 4, 2, 3 ] 
[ 5, 1, 6 ] 
[ 1, 2, 8 ] 
[ 4, 2, 8 ] 
[ 2, 5, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 2 ] - [ 8, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 
[ 1, 2, 5 ] - [ 1, 6, 5 ] 

Cartan matrix

(1 1 1 0 1 1 0 0)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 1 0 0 0)
(1 0 0 0 1 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1551    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1188    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1211    permutation [ 8, 5, 1, 7, 6, 4, 3, 2 ]
vertex  5 -> Algebra  864    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  859    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  858    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1369

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 4 ], [ 3, 2 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 3, 2, 1 ] 
[ 6, 5, 2, 1 ] 
[ 4, 5, 2 ] 
[ 2, 1, 3 ] 
[ 5, 2, 4 ] 
[ 5, 2, 1, 6 ] 
[ 1, 3, 2 ] - [ 1, 6, 5, 2 ] 
[ 2, 1, 6, 5 ] - [ 2, 4, 5 ] 

Cartan matrix

(1 1 1 0 1 1 1 0)
(1 1 0 1 1 1 1 0)
(0 1 1 1 0 0 0 0)
(0 0 0 1 1 0 0 0)
(1 1 0 0 1 0 0 0)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra  859    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1506    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1519    permutation [ 8, 5, 4, 6, 7, 2, 3, 1 ]
vertex  7 -> Algebra 1551    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  869    permutation [ 1, 5, 3, 4, 8, 6, 7, 2 ]

Algebra 1374

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 5, 2, 8, 1 ] 
[ 3, 4, 2 ] 
[ 4, 2, 3 ] 
[ 2, 8, 1, 5 ] 
[ 1, 5, 2, 8 ] 
[ 4, 2, 8 ] 
[ 8, 1, 5, 2 ] - [ 8, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 

Cartan matrix

(1 1 1 0 1 0 0 0)
(1 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 1 1 1 1 1 1 1)
(0 1 1 1 1 0 1 1)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  3 -> Algebra 1195    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1448    permutation [ 8, 1, 6, 7, 5, 4, 3, 2 ]
vertex  6 -> Algebra 1377    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  861    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1377

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 5, 2, 8, 1 ] 
[ 3, 4, 2 ] 
[ 4, 2, 3 ] 
[ 2, 8, 1, 5 ] 
[ 1, 5, 2, 8 ] 
[ 4, 2, 8 ] 
[ 8, 1, 5, 2 ] - [ 8, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 

Cartan matrix

(1 1 1 0 1 0 0 0)
(1 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  3 -> Algebra 1014    permutation [ 1, 5, 3, 8, 4, 6, 7, 2 ]
vertex  4 -> Algebra 1426    permutation [ 8, 1, 6, 7, 5, 4, 3, 2 ]
vertex  6 -> Algebra  864    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1374    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  863    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1380

Quiver

[ 1, 2 ], [ 1, 6 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 8 ], [ 7, 6 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 5, 8, 1 ] 
[ 5, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 4 ] 
[ 1, 2, 5, 8 ] 
[ 8, 1, 2, 5 ] - [ 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 0 0 1 1 0 0)
(0 1 0 0 1 0 0 1)
(1 0 1 1 1 1 0 1)
(1 1 0 1 0 1 0 1)
(1 0 0 0 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 1 1 0 1)

Good mutations

vertex  3 -> Algebra 1410    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra 1233    permutation [ 4, 2, 5, 1, 7, 6, 3, 8 ]
vertex  5 -> Algebra 1360    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra  866    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  952    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]

Algebra 1381

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 5, 8, 1 ] 
[ 5, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 4 ] 
[ 1, 2, 5, 8 ] 
[ 8, 1, 2, 5 ] - [ 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 0 0 1 0 0 1)
(1 0 1 1 1 0 0 1)
(1 1 0 1 0 0 0 1)
(1 0 0 0 1 0 0 1)
(1 1 0 0 1 1 0 0)
(1 1 0 0 1 1 1 0)
(1 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  868    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1411    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra 1208    permutation [ 4, 2, 5, 7, 6, 1, 3, 8 ]
vertex  5 -> Algebra 1361    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra  866    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1387

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 6, 2 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 3, 8, 1 ] 
[ 6, 2, 8, 1 ] 
[ 8, 1, 3 ] 
[ 2, 8, 4 ] 
[ 2, 8, 1, 6 ] 
[ 4, 2, 8 ] 
[ 8, 1, 6, 2 ] - [ 8, 4, 2 ] 
[ 1, 3, 8 ] - [ 1, 6, 2, 8 ] 

Cartan matrix

(1 1 1 0 1 1 0 1)
(1 1 0 0 1 0 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 0 0 1 1 0 1)
(0 1 0 0 1 1 1 1)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  3 -> Algebra 1484    permutation [ 3, 1, 7, 5, 6, 2, 4, 8 ]
vertex  4 -> Algebra 1509    permutation [ 8, 2, 4, 7, 6, 5, 3, 1 ]
vertex  5 -> Algebra 1551    permutation [ 1, 8, 3, 4, 2, 6, 7, 5 ]
vertex  7 -> Algebra  869    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  868    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1389

Quiver

[ 1, 6 ], [ 2, 8 ], [ 3, 1 ], [ 4, 2 ], [ 6, 2 ], [ 6, 7 ], [ 8, 3 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 6, 2, 8, 3, 1 ] 
[ 1, 6, 2, 8, 3 ] 
[ 2, 8, 4 ] 
[ 2, 8, 3, 1, 6 ] 
[ 3, 1, 6, 2, 8 ] 
[ 4, 2, 8 ] 
[ 8, 3, 1, 6, 2 ] - [ 8, 4, 2 ] 

Cartan matrix

(1 1 0 0 1 1 1 1)
(1 1 1 0 1 0 0 1)
(1 1 1 0 0 1 1 0)
(0 1 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  3 -> Algebra  869    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1506    permutation [ 1, 8, 3, 4, 2, 6, 7, 5 ]
vertex  6 -> Algebra 1529    permutation [ 3, 2, 1, 7, 6, 8, 4, 5 ]
vertex  7 -> Algebra 1484    permutation [ 3, 1, 7, 5, 6, 2, 4, 8 ]
vertex  8 -> Algebra  890    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1399

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 5 ], [ 2, 6 ], [ 3, 2 ], [ 6, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 3, 2, 6, 1 ] 
[ 7, 6, 1 ] 
[ 6, 1, 3, 2 ] 
[ 2, 6, 1, 3 ] 
[ 8, 7, 6 ] 
[ 7, 6, 8 ] 
[ 1, 3, 2, 6 ] - [ 1, 7, 6 ] 
[ 6, 1, 7 ] - [ 6, 8, 7 ] 

Cartan matrix

(1 1 1 0 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(1 0 1 1 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1425    permutation [ 7, 3, 2, 5, 1, 8, 4, 6 ]
vertex  2 -> Algebra 1218    permutation [ 1, 2, 3, 5, 7, 8, 4, 6 ]
vertex  4 -> Algebra 1429    permutation [ 8, 1, 3, 2, 5, 7, 4, 6 ]
vertex  5 -> Algebra 1409    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra  911    permutation [ 1, 3, 2, 5, 7, 8, 4, 6 ]

Algebra 1409

Quiver

[ 1, 3 ], [ 1, 7 ], [ 2, 5 ], [ 3, 5 ], [ 5, 6 ], [ 6, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 3, 5, 6, 1 ] 
[ 7, 6, 1 ] 
[ 5, 6, 1, 3 ] 
[ 6, 1, 3, 5 ] 
[ 8, 7, 6 ] 
[ 7, 6, 8 ] 
[ 1, 3, 5, 6 ] - [ 1, 7, 6 ] 
[ 6, 1, 7 ] - [ 6, 8, 7 ] 

Cartan matrix

(1 0 1 0 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 0 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(1 0 0 1 1 1 1 1)
(1 0 1 1 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1446    permutation [ 7, 3, 2, 5, 1, 8, 4, 6 ]
vertex  2 -> Algebra 1399    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  4 -> Algebra 1413    permutation [ 8, 1, 3, 2, 5, 7, 4, 6 ]
vertex  7 -> Algebra  954    permutation [ 1, 3, 2, 5, 7, 8, 4, 6 ]

Algebra 1410

Quiver

[ 1, 2 ], [ 1, 6 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 7, 6 ], [ 8, 1 ]

Relations

[ 2, 3, 5, 8, 1 ] 
[ 3, 5, 8, 1, 2 ] 
[ 5, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 5 ] 
[ 1, 2, 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 1 1 0 0)
(0 1 1 0 1 0 0 1)
(1 0 1 0 1 1 0 1)
(1 1 0 1 1 1 0 1)
(1 1 0 0 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1413    permutation [ 6, 2, 3, 4, 5, 1, 7, 8 ]
vertex  4 -> Algebra 1424    permutation [ 2, 3, 5, 4, 1, 6, 7, 8 ]
vertex  5 -> Algebra 1380    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra  887    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  954    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]

Algebra 1411

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ]

Relations

[ 2, 3, 5, 8, 1 ] 
[ 3, 5, 8, 1, 2 ] 
[ 5, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 5 ] 
[ 1, 2, 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 0)
(0 1 1 0 1 0 0 1)
(1 0 1 0 1 0 0 1)
(1 1 0 1 1 0 0 1)
(1 1 0 0 1 0 0 1)
(1 1 1 0 1 1 0 0)
(1 1 1 0 1 1 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  889    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1427    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1381    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra  887    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1413

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 6, 8, 1 ] 
[ 3, 5, 8, 2 ] 
[ 6, 8, 2 ] 
[ 5, 8, 2, 3 ] 
[ 8, 2, 3, 5 ] 
[ 1, 6, 8 ] 
[ 8, 1, 6 ] - [ 8, 2, 6 ] 
[ 2, 3, 5, 8 ] - [ 2, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 0)
(0 1 1 0 1 1 0 1)
(1 0 1 0 1 0 0 1)
(1 1 0 1 1 1 0 1)
(1 1 0 0 1 1 0 1)
(0 0 0 0 0 1 0 1)
(1 0 0 0 0 1 1 0)
(1 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  888    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1417    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  4 -> Algebra 1429    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1410    permutation [ 6, 2, 3, 4, 5, 1, 7, 8 ]
vertex  7 -> Algebra 1409    permutation [ 2, 4, 3, 7, 5, 8, 6, 1 ]

Algebra 1417

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 8 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 6, 8, 1 ] 
[ 6, 8, 1, 2 ] 
[ 5, 8, 3 ] 
[ 6, 8, 3 ] 
[ 8, 3, 5 ] 
[ 1, 2, 6, 8 ] 
[ 8, 1, 2, 6 ] - [ 8, 3, 6 ] 
[ 3, 5, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 1 0 0 0 1 0 0)
(0 1 0 0 0 1 0 1)
(1 0 1 0 1 1 0 1)
(1 1 0 1 1 0 0 1)
(1 1 0 0 1 0 0 1)
(1 0 0 0 0 1 0 1)
(1 1 0 0 0 1 1 0)
(1 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  891    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1420    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra 1430    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1413    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  7 -> Algebra 1446    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]

Algebra 1420

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 6 ], [ 4, 5 ], [ 5, 6 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ]

Relations

[ 2, 3, 6, 8, 1 ] 
[ 3, 6, 8, 1, 2 ] 
[ 6, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 6 ] 
[ 1, 2, 3, 6, 8 ] 

Cartan matrix

(1 1 1 0 0 1 0 0)
(0 1 1 0 0 1 0 1)
(1 0 1 0 0 1 0 1)
(1 1 0 1 1 1 0 1)
(1 1 0 0 1 1 0 1)
(1 1 0 0 0 1 0 1)
(1 1 1 0 0 1 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  896    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1431    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1417    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra 1448    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]

Algebra 1424

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 2, 3, 8, 5, 1 ] 
[ 3, 8, 5, 1, 2 ] 
[ 8, 5, 1, 2, 3 ] 
[ 1, 2, 3, 8, 5 ] 
[ 5, 1, 2, 3, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(0 1 1 1 1 1 0 1)
(1 0 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(1 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 0 1 1 0 1)

Good mutations

vertex  3 -> Algebra 1217    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1410    permutation [ 5, 1, 2, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra 1429    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  6 -> Algebra  915    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  911    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1425

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 5, 8, 6, 1 ] 
[ 3, 8, 2 ] 
[ 5, 8, 2 ] 
[ 8, 2, 3 ] 
[ 1, 5, 8, 6 ] 
[ 6, 1, 5, 8 ] 
[ 8, 2, 5 ] - [ 8, 6, 1, 5 ] 
[ 2, 3, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 1 0 0 1)
(0 1 1 1 1 1 1 1)
(1 0 1 1 0 1 1 1)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 1 1 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1426    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1219    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1446    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1399    permutation [ 5, 3, 2, 7, 4, 8, 1, 6 ]
vertex  7 -> Algebra 1430    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]

Algebra 1426

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 2, 5, 8, 6, 1 ] 
[ 5, 8, 6, 1, 2 ] 
[ 8, 6, 1, 2, 5 ] 
[ 1, 2, 5, 8, 6 ] 
[ 6, 1, 2, 5, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 1)
(0 1 0 0 1 1 1 1)
(1 0 1 1 1 1 1 1)
(0 0 0 1 0 0 0 0)
(1 0 0 0 1 1 1 1)
(1 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 0 1 1 1)

Good mutations

vertex  3 -> Algebra 1277    permutation [ 2, 8, 1, 7, 5, 3, 4, 6 ]
vertex  4 -> Algebra 1448    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1425    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1377    permutation [ 2, 8, 7, 6, 5, 3, 4, 1 ]
vertex  7 -> Algebra 1431    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]

Algebra 1427

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ]

Relations

[ 2, 3, 4, 8, 1 ] 
[ 3, 4, 8, 1, 2 ] 
[ 4, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 4 ] 
[ 1, 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(0 1 1 1 1 0 0 1)
(1 0 1 1 1 0 0 1)
(1 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(1 1 1 1 1 1 0 0)
(1 1 1 1 1 1 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  917    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1309    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1411    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  915    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1429

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 6, 8, 1 ] 
[ 3, 4, 8, 2 ] 
[ 6, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 1, 6, 8 ] 
[ 8, 1, 6 ] - [ 8, 2, 6 ] 
[ 2, 3, 4, 8 ] - [ 2, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 0)
(0 1 1 1 1 1 0 1)
(1 0 1 1 1 0 0 1)
(1 1 0 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 0 1 0 1)
(1 0 0 0 0 1 1 0)
(1 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  916    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1430    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  4 -> Algebra 1310    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1413    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1424    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  7 -> Algebra 1399    permutation [ 2, 4, 3, 7, 5, 8, 6, 1 ]

Algebra 1430

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 3, 6 ], [ 4, 5 ], [ 4, 8 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 6, 8, 1 ] 
[ 6, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 6, 8, 3 ] 
[ 8, 3, 4 ] 
[ 1, 2, 6, 8 ] 
[ 8, 1, 2, 6 ] - [ 8, 3, 6 ] 
[ 3, 4, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 1 0 0 0 1 0 0)
(0 1 0 0 0 1 0 1)
(1 0 1 1 1 1 0 1)
(1 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(1 0 0 0 0 1 0 1)
(1 1 0 0 0 1 1 0)
(1 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  918    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1431    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra 1314    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1417    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1429    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  7 -> Algebra 1425    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]

Algebra 1431

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 6 ], [ 4, 5 ], [ 4, 6 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ]

Relations

[ 2, 3, 6, 8, 1 ] 
[ 3, 6, 8, 1, 2 ] 
[ 6, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 6 ] 
[ 1, 2, 3, 6, 8 ] 

Cartan matrix

(1 1 1 0 0 1 0 0)
(0 1 1 0 0 1 0 1)
(1 0 1 0 0 1 0 1)
(1 1 0 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(1 1 0 0 0 1 0 1)
(1 1 1 0 0 1 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  921    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1432    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra 1420    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1430    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra 1426    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]

Algebra 1432

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 7, 1 ], [ 8, 1 ]

Relations

[ 2, 3, 4, 8, 1 ] 
[ 3, 4, 8, 1, 2 ] 
[ 4, 8, 1, 2, 3 ] 
[ 8, 1, 2, 3, 4 ] 
[ 1, 2, 3, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 1 0 0)
(0 1 1 1 0 1 0 1)
(1 0 1 1 0 1 0 1)
(1 1 0 1 0 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(1 1 1 1 0 1 1 0)
(1 1 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  927    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1324    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1163    permutation [ 3, 1, 2, 8, 4, 6, 5, 7 ]
vertex  6 -> Algebra 1431    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra 1277    permutation [ 3, 8, 2, 7, 4, 6, 5, 1 ]

Algebra 1445

Quiver

[ 1, 6 ], [ 2, 4 ], [ 2, 8 ], [ 3, 6 ], [ 4, 5 ], [ 5, 1 ], [ 5, 2 ], [ 6, 7 ], [ 6, 8 ], [ 8, 3 ], [ 8, 5 ]

Relations

[ 6, 8, 5, 1 ] 
[ 4, 5, 2 ] 
[ 8, 5, 2 ] 
[ 6, 8, 3 ] 
[ 5, 2, 4 ] 
[ 1, 6, 8, 5 ] 
[ 3, 6, 8 ] 
[ 2, 4, 5 ] - [ 2, 8, 5 ] 
[ 8, 3, 6 ] - [ 8, 5, 1, 6 ] 
[ 5, 1, 6, 8 ] - [ 5, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 1 1 1)
(1 1 1 1 1 1 1 1)
(0 0 1 0 0 1 1 0)
(1 0 0 1 1 1 1 0)
(1 1 0 0 1 1 1 1)
(0 0 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 0 1 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1509    permutation [ 6, 5, 1, 4, 2, 7, 3, 8 ]
vertex  6 -> Algebra 1505    permutation [ 6, 5, 8, 4, 1, 7, 3, 2 ]
vertex  7 -> Algebra 1471    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra  953    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1446

Quiver

[ 1, 5 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 5, 8, 6, 1 ] 
[ 4, 8, 2 ] 
[ 5, 8, 2 ] 
[ 8, 2, 4 ] 
[ 1, 5, 8, 6 ] 
[ 6, 1, 5, 8 ] 
[ 8, 2, 5 ] - [ 8, 6, 1, 5 ] 
[ 2, 4, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 1 0 0 1)
(0 1 0 1 1 1 1 1)
(1 0 1 1 0 1 1 1)
(1 0 0 1 0 1 1 1)
(0 0 0 0 1 1 1 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1448    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1425    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1409    permutation [ 5, 3, 2, 7, 4, 8, 1, 6 ]
vertex  7 -> Algebra 1417    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]

Algebra 1448

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 2, 5, 8, 6, 1 ] 
[ 5, 8, 6, 1, 2 ] 
[ 8, 6, 1, 2, 5 ] 
[ 1, 2, 5, 8, 6 ] 
[ 6, 1, 2, 5, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 1)
(0 1 0 0 1 1 1 1)
(1 0 1 1 1 1 1 1)
(1 0 0 1 1 1 1 1)
(1 0 0 0 1 1 1 1)
(1 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 0 1 1 1)

Good mutations

vertex  3 -> Algebra 1426    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1446    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1374    permutation [ 2, 8, 7, 6, 5, 3, 4, 1 ]
vertex  7 -> Algebra 1420    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]

Algebra 1453

Quiver

[ 2, 1 ], [ 2, 4 ], [ 2, 7 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 2, 4, 3 ] 
[ 3, 2, 4 ] 
[ 5, 6, 2, 4 ] 
[ 6, 2, 4, 5 ] 
[ 6, 2, 7 ] 
[ 4, 3, 2 ] - [ 4, 5, 6, 2 ] 
[ 2, 4, 5, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 1 1 1 1 0)
(1 1 1 0 0 0 1 0)
(1 1 1 1 1 1 0 0)
(1 1 0 0 1 1 0 0)
(1 1 0 1 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1287    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1536    permutation [ 3, 7, 6, 4, 5, 2, 8, 1 ]
vertex  7 -> Algebra 1260    permutation [ 6, 2, 1, 4, 8, 3, 5, 7 ]
vertex  8 -> Algebra 1049    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1454

Quiver

[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 4, 5, 6, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 6, 2, 3, 4 ] 
[ 2, 3, 4, 5, 6 ] 
[ 7, 5, 6 ] 
[ 5, 6, 7 ] 
[ 2, 3, 8 ] 
[ 3, 4, 5, 6, 2 ] - [ 3, 8, 2 ] 
[ 6, 2, 3, 4, 5 ] - [ 6, 7, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 0 0 0)
(1 1 1 1 1 1 0 1)
(1 1 0 1 1 1 0 0)
(1 1 1 0 1 1 0 0)
(1 1 1 1 1 1 1 0)
(0 0 0 0 1 0 1 0)
(1 1 0 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1289    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1000    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1462

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 1 ], [ 6, 3 ], [ 7, 2 ], [ 8, 6 ]

Relations

[ 2, 8, 6, 1 ] 
[ 8, 6, 1, 2 ] 
[ 8, 6, 3 ] 
[ 5, 3, 4 ] 
[ 6, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 2, 8, 6 ] 
[ 4, 5, 3 ] - [ 4, 6, 3 ] 
[ 3, 4, 6 ] - [ 3, 8, 6 ] 
[ 6, 1, 2, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 0 0 1 0 1)
(1 0 1 1 0 1 0 1)
(1 1 1 1 1 1 0 1)
(0 0 1 0 1 0 0 1)
(1 1 1 0 0 1 0 1)
(0 1 0 0 0 1 1 1)
(1 0 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1536    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1572    permutation [ 6, 1, 3, 7, 2, 8, 5, 4 ]
vertex  4 -> Algebra 1204    permutation [ 1, 3, 8, 5, 4, 2, 7, 6 ]
vertex  6 -> Algebra 1188    permutation [ 1, 3, 6, 5, 8, 2, 7, 4 ]
vertex  7 -> Algebra 1190    permutation [ 1, 3, 6, 5, 8, 2, 7, 4 ]
vertex  8 -> Algebra 1015    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1471

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 5 ], [ 3, 8 ], [ 4, 2 ], [ 5, 6 ], [ 6, 1 ], [ 6, 3 ], [ 7, 2 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 2, 8, 6, 1 ] 
[ 5, 6, 3 ] 
[ 8, 6, 3 ] 
[ 2, 8, 4 ] 
[ 6, 3, 5 ] 
[ 1, 2, 8, 6 ] 
[ 4, 2, 8 ] 
[ 8, 4, 2 ] - [ 8, 6, 1, 2 ] 
[ 3, 5, 6 ] - [ 3, 8, 6 ] 
[ 6, 1, 2, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 0 0 1 0 1)
(1 1 1 1 1 1 0 1)
(0 1 0 1 0 0 0 0)
(1 1 0 0 1 1 0 0)
(1 1 1 0 0 1 0 1)
(0 1 0 0 0 1 1 1)
(1 1 0 1 0 1 0 1)

Good mutations

vertex  2 -> Algebra 1472    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1511    permutation [ 7, 6, 1, 5, 3, 2, 4, 8 ]
vertex  7 -> Algebra 1445    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1047    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1472

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 5 ], [ 5, 6 ], [ 6, 1 ], [ 6, 3 ], [ 7, 2 ], [ 8, 1 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 2, 6, 3 ] 
[ 5, 6, 3 ] 
[ 6, 3, 5 ] 
[ 1, 2, 6 ] 
[ 2, 8, 7 ] 
[ 1, 2, 8 ] 
[ 7, 2, 8 ] 
[ 2, 6, 1 ] - [ 2, 8, 1 ] 
[ 6, 1, 2 ] - [ 6, 3, 2 ] 
[ 8, 1, 2 ] - [ 8, 7, 2 ] 
[ 3, 2, 6 ] - [ 3, 5, 6 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(1 1 0 1 0 1 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(1 0 0 0 1 1 0 0)
(1 1 1 0 0 1 0 0)
(0 1 0 0 0 1 1 0)
(1 1 0 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1219    permutation [ 7, 6, 3, 5, 2, 8, 4, 1 ]
vertex  2 -> Algebra 1049    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1205    permutation [ 7, 6, 1, 5, 3, 8, 4, 2 ]
vertex  4 -> Algebra 1536    permutation [ 8, 7, 6, 3, 5, 2, 4, 1 ]
vertex  7 -> Algebra 1190    permutation [ 7, 6, 2, 5, 1, 8, 4, 3 ]
vertex  8 -> Algebra 1471    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1484

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 5, 6 ], [ 6, 8 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 2, 5, 6, 8, 1 ] 
[ 5, 6, 8, 1, 2 ] 
[ 6, 8, 1, 2, 5 ] 
[ 6, 8, 7 ] 
[ 1, 2, 5, 6, 8 ] 
[ 7, 6, 8 ] 
[ 8, 1, 2, 5, 6 ] - [ 8, 7, 6 ] 

Cartan matrix

(1 1 0 0 1 1 0 0)
(0 1 0 1 1 1 0 1)
(1 0 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(1 0 0 1 1 1 0 1)
(1 1 0 1 0 1 0 1)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1387    permutation [ 2, 6, 1, 7, 4, 5, 3, 8 ]
vertex  3 -> Algebra 1389    permutation [ 2, 6, 1, 7, 4, 5, 3, 8 ]
vertex  4 -> Algebra 1572    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  8 -> Algebra 1349    permutation [ 1, 3, 2, 5, 6, 8, 7, 4 ]

Algebra 1491

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 5, 6 ], [ 6, 8 ], [ 7, 6 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 2, 3, 1 ] 
[ 5, 6, 8, 2 ] 
[ 1, 2, 3 ] 
[ 8, 2, 3 ] 
[ 6, 8, 2, 5 ] 
[ 6, 8, 7 ] 
[ 7, 6, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 5, 6 ] - [ 8, 7, 6 ] 
[ 2, 3, 8 ] - [ 2, 5, 6, 8 ] 

Cartan matrix

(1 1 0 0 1 1 0 0)
(0 1 1 1 1 1 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 1 0 1)
(0 1 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  3 -> Algebra 1289    permutation [ 1, 3, 2, 5, 6, 8, 7, 4 ]
vertex  4 -> Algebra 1496    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1529    permutation [ 1, 8, 2, 5, 6, 3, 7, 4 ]

Algebra 1496

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 6 ], [ 6, 8 ], [ 7, 6 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 2, 4, 1 ] 
[ 5, 6, 8, 2 ] 
[ 1, 2, 4 ] 
[ 8, 2, 4 ] 
[ 6, 8, 2, 5 ] 
[ 6, 8, 7 ] 
[ 7, 6, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 8, 2, 5, 6 ] - [ 8, 7, 6 ] 
[ 2, 4, 8 ] - [ 2, 5, 6, 8 ] 

Cartan matrix

(1 1 0 0 1 1 0 0)
(0 1 0 1 1 1 0 1)
(1 1 1 1 1 1 1 1)
(1 1 0 1 1 1 1 1)
(0 0 0 0 1 1 0 1)
(0 1 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  3 -> Algebra 1491    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1549    permutation [ 8, 3, 7, 4, 1, 2, 6, 5 ]

Algebra 1505

Quiver

[ 1, 5 ], [ 1, 7 ], [ 2, 5 ], [ 2, 8 ], [ 3, 1 ], [ 3, 2 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 1 ], [ 7, 6 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 7, 6, 1 ] 
[ 5, 3, 2 ] 
[ 1, 5, 3 ] 
[ 2, 8, 4 ] 
[ 6, 1, 5 ] 
[ 6, 1, 7 ] 
[ 3, 2, 8 ] 
[ 4, 2, 8 ] 
[ 5, 3, 1 ] - [ 5, 6, 1 ] 
[ 8, 3, 2 ] - [ 8, 4, 2 ] 
[ 2, 5, 3 ] - [ 2, 8, 3 ] 
[ 3, 1, 5 ] - [ 3, 2, 5 ] 
[ 1, 5, 6 ] - [ 1, 7, 6 ] 

Cartan matrix

(1 0 0 0 1 1 1 0)
(1 1 1 0 1 1 0 1)
(1 1 1 0 1 1 1 0)
(0 1 0 1 1 1 0 0)
(1 0 1 0 1 1 0 0)
(1 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1445    permutation [ 5, 8, 7, 4, 2, 1, 6, 3 ]
vertex  2 -> Algebra 1549    permutation [ 5, 8, 4, 2, 3, 1, 6, 7 ]
vertex  6 -> Algebra 1190    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1202    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1506

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 4 ], [ 3, 1 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 6, 5, 2, 3, 1 ] 
[ 3, 1, 6, 5, 2 ] 
[ 4, 5, 2 ] 
[ 1, 6, 5, 2, 3 ] 
[ 5, 2, 4 ] 
[ 5, 2, 3, 1, 6 ] 
[ 2, 3, 1, 6, 5 ] - [ 2, 4, 5 ] 

Cartan matrix

(1 1 0 0 1 1 1 0)
(1 1 1 1 1 1 1 0)
(1 0 1 0 1 1 1 0)
(0 0 0 1 1 0 0 0)
(1 1 1 0 1 0 0 0)
(0 1 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1190    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1369    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1549    permutation [ 5, 8, 4, 2, 3, 1, 6, 7 ]
vertex  7 -> Algebra 1572    permutation [ 3, 1, 2, 7, 6, 5, 4, 8 ]
vertex  8 -> Algebra 1389    permutation [ 1, 5, 3, 4, 8, 6, 7, 2 ]

Algebra 1509

Quiver

[ 1, 6 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 5 ], [ 5, 2 ], [ 7, 1 ], [ 8, 5 ], [ 8, 7 ]

Relations

[ 3, 1, 8, 5, 2 ] 
[ 1, 8, 5, 2, 3 ] 
[ 2, 3, 1, 8, 5 ] 
[ 1, 8, 7 ] 
[ 5, 2, 3, 1, 8 ] 
[ 7, 1, 8 ] 
[ 8, 5, 2, 3, 1 ] - [ 8, 7, 1 ] 

Cartan matrix

(1 1 0 0 1 1 0 1)
(1 1 1 0 0 1 0 1)
(1 0 1 0 1 1 0 1)
(1 1 1 1 1 1 0 0)
(1 1 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(1 0 0 0 0 1 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1202    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1387    permutation [ 8, 2, 7, 3, 6, 5, 4, 1 ]
vertex  4 -> Algebra 1282    permutation [ 8, 2, 1, 7, 6, 5, 4, 3 ]
vertex  5 -> Algebra 1445    permutation [ 3, 5, 7, 4, 2, 1, 6, 8 ]
vertex  6 -> Algebra 1511    permutation [ 6, 2, 3, 4, 5, 1, 7, 8 ]

Algebra 1510

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 1 ], [ 6, 3 ], [ 7, 6 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 8, 6, 1 ] 
[ 3, 8, 5, 2 ] 
[ 2, 3, 8, 5 ] 
[ 1, 8, 6 ] 
[ 3, 8, 6 ] 
[ 5, 2, 3, 8 ] 
[ 8, 5, 2, 3 ] - [ 8, 6, 3 ] 
[ 6, 1, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 0 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 1 1 0 1 0 0 0)
(1 0 1 0 1 1 0 1)
(1 0 1 0 1 1 1 1)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1204    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1324    permutation [ 6, 1, 2, 8, 4, 5, 7, 3 ]
vertex  4 -> Algebra 1518    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1536    permutation [ 6, 1, 2, 5, 4, 8, 7, 3 ]
vertex  7 -> Algebra 1205    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1511

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 6 ], [ 4, 5 ], [ 5, 2 ], [ 6, 8 ], [ 7, 6 ], [ 8, 5 ], [ 8, 7 ]

Relations

[ 3, 6, 8, 5, 2 ] 
[ 6, 8, 5, 2, 3 ] 
[ 2, 3, 6, 8, 5 ] 
[ 6, 8, 7 ] 
[ 5, 2, 3, 6, 8 ] 
[ 7, 6, 8 ] 
[ 8, 5, 2, 3, 6 ] - [ 8, 7, 6 ] 

Cartan matrix

(1 1 0 0 1 1 0 1)
(0 1 1 0 0 1 0 1)
(0 0 1 0 1 1 0 1)
(0 1 1 1 1 1 0 0)
(0 1 1 0 1 1 0 0)
(0 1 0 0 1 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1509    permutation [ 6, 2, 3, 4, 5, 1, 7, 8 ]
vertex  3 -> Algebra 1551    permutation [ 8, 6, 7, 3, 2, 5, 4, 1 ]
vertex  4 -> Algebra 1519    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1471    permutation [ 3, 6, 5, 7, 4, 2, 1, 8 ]
vertex  6 -> Algebra 1205    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1518

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 1 ], [ 6, 3 ], [ 7, 6 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 8, 6, 1 ] 
[ 3, 8, 4, 2 ] 
[ 2, 3, 8, 4 ] 
[ 1, 8, 6 ] 
[ 3, 8, 6 ] 
[ 4, 2, 3, 8 ] 
[ 8, 4, 2, 3 ] - [ 8, 6, 3 ] 
[ 6, 1, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 1 1 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 0 1 1 1 1 0 1)
(1 0 1 1 1 1 1 1)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1226    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1336    permutation [ 6, 1, 2, 8, 4, 5, 7, 3 ]
vertex  5 -> Algebra 1510    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra 1227    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1519

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 6 ], [ 4, 2 ], [ 4, 5 ], [ 6, 8 ], [ 7, 6 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 3, 6, 8, 4, 2 ] 
[ 6, 8, 4, 2, 3 ] 
[ 2, 3, 6, 8, 4 ] 
[ 6, 8, 7 ] 
[ 4, 2, 3, 6, 8 ] 
[ 7, 6, 8 ] 
[ 8, 4, 2, 3, 6 ] - [ 8, 7, 6 ] 

Cartan matrix

(1 1 0 1 1 1 0 1)
(0 1 1 0 0 1 0 1)
(0 0 1 1 1 1 0 1)
(0 1 1 1 1 1 0 0)
(0 0 0 0 1 0 0 0)
(0 1 0 1 1 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1282    permutation [ 8, 2, 6, 7, 1, 4, 5, 3 ]
vertex  3 -> Algebra 1369    permutation [ 8, 6, 7, 3, 2, 4, 5, 1 ]
vertex  5 -> Algebra 1511    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1227    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1529

Quiver

[ 1, 3 ], [ 2, 5 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 6, 1 ], [ 6, 7 ], [ 6, 8 ], [ 7, 2 ]

Relations

[ 3, 2, 6, 1 ] 
[ 5, 3, 2 ] 
[ 4, 5, 3 ] 
[ 5, 3, 4 ] 
[ 1, 3, 2, 6 ] 
[ 7, 2, 6 ] 
[ 2, 6, 7 ] 
[ 6, 1, 3, 2 ] - [ 6, 7, 2 ] 
[ 2, 5, 3 ] - [ 2, 6, 1, 3 ] 
[ 3, 2, 5 ] - [ 3, 4, 5 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(1 1 1 0 1 1 0 1)
(0 1 1 1 1 1 0 1)
(0 0 0 1 1 0 0 0)
(0 0 1 0 1 0 0 0)
(1 1 1 1 1 1 1 1)
(0 1 0 0 1 0 1 0)
(0 0 0 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1491    permutation [ 1, 3, 6, 8, 4, 5, 7, 2 ]
vertex  5 -> Algebra 1389    permutation [ 3, 2, 1, 7, 8, 5, 4, 6 ]
vertex  6 -> Algebra 1290    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1549    permutation [ 2, 8, 7, 6, 1, 3, 5, 4 ]

Algebra 1536

Quiver

[ 1, 2 ], [ 1, 8 ], [ 2, 6 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 1 ], [ 6, 3 ], [ 7, 1 ], [ 8, 6 ]

Relations

[ 2, 6, 1 ] 
[ 8, 6, 1 ] 
[ 6, 1, 2 ] 
[ 8, 6, 3 ] 
[ 5, 3, 4 ] 
[ 6, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 5, 3 ] - [ 4, 6, 3 ] 
[ 1, 2, 6 ] - [ 1, 8, 6 ] 
[ 3, 4, 6 ] - [ 3, 8, 6 ] 
[ 6, 1, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 1 0 1)
(0 1 1 0 0 1 0 0)
(0 0 1 1 0 1 0 1)
(1 0 1 1 1 1 0 1)
(0 0 1 0 1 0 0 1)
(1 0 1 0 0 1 0 1)
(1 1 0 0 0 1 1 1)
(0 0 0 0 0 1 0 1)

Good mutations

vertex  2 -> Algebra 1462    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1510    permutation [ 2, 3, 8, 5, 4, 1, 7, 6 ]
vertex  6 -> Algebra 1453    permutation [ 8, 6, 1, 4, 5, 3, 2, 7 ]
vertex  7 -> Algebra 1472    permutation [ 8, 6, 4, 7, 5, 3, 2, 1 ]
vertex  8 -> Algebra 1314    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1549

Quiver

[ 1, 4 ], [ 1, 7 ], [ 2, 4 ], [ 3, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 7 ]

Relations

[ 7, 6, 1 ] 
[ 1, 4, 3 ] 
[ 3, 1, 4 ] 
[ 5, 6, 1, 4 ] 
[ 6, 1, 4, 5 ] 
[ 8, 7, 6 ] 
[ 7, 6, 8 ] 
[ 4, 3, 1 ] - [ 4, 5, 6, 1 ] 
[ 1, 4, 5, 6 ] - [ 1, 7, 6 ] 
[ 6, 1, 7 ] - [ 6, 8, 7 ] 

Cartan matrix

(1 0 0 1 1 1 1 0)
(1 1 1 1 1 1 1 1)
(1 0 1 0 0 0 1 0)
(1 0 1 1 1 1 1 1)
(1 0 0 0 1 1 1 1)
(1 0 0 1 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1496    permutation [ 5, 6, 2, 4, 8, 7, 3, 1 ]
vertex  2 -> Algebra 1529    permutation [ 5, 1, 6, 8, 7, 4, 3, 2 ]
vertex  4 -> Algebra 1505    permutation [ 6, 4, 5, 3, 1, 7, 8, 2 ]
vertex  7 -> Algebra 1506    permutation [ 6, 4, 5, 3, 1, 7, 8, 2 ]

Algebra 1551

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 4 ], [ 3, 2 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 3, 2, 1 ] 
[ 6, 5, 2, 1 ] 
[ 4, 5, 2 ] 
[ 2, 1, 3 ] 
[ 5, 2, 4 ] 
[ 5, 2, 1, 6 ] 
[ 1, 3, 2 ] - [ 1, 6, 5, 2 ] 
[ 2, 1, 6, 5 ] - [ 2, 4, 5 ] 

Cartan matrix

(1 1 1 0 1 1 0 0)
(1 1 0 1 1 1 0 0)
(0 1 1 1 0 0 0 0)
(0 0 0 1 1 0 0 0)
(1 1 0 0 1 0 0 0)
(0 1 0 0 1 1 0 0)
(0 1 0 0 1 1 1 0)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1367    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1572    permutation [ 3, 1, 2, 7, 6, 5, 4, 8 ]
vertex  4 -> Algebra 1511    permutation [ 8, 5, 4, 7, 6, 2, 3, 1 ]
vertex  7 -> Algebra 1369    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1387    permutation [ 1, 5, 3, 4, 8, 6, 7, 2 ]

Algebra 1572

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 1 ], [ 3, 7 ], [ 4, 5 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 2, 5, 6, 3, 1 ] 
[ 5, 6, 3, 1, 2 ] 
[ 1, 2, 5, 6, 3 ] 
[ 7, 6, 3 ] 
[ 6, 3, 1, 2, 5 ] 
[ 6, 3, 7 ] 
[ 3, 1, 2, 5, 6 ] - [ 3, 7, 6 ] 

Cartan matrix

(1 1 0 0 1 1 0 0)
(0 1 1 0 1 1 0 0)
(1 1 1 0 1 1 1 0)
(1 0 1 1 1 1 0 0)
(1 0 1 0 1 1 0 0)
(1 1 1 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1551    permutation [ 2, 3, 1, 7, 6, 5, 4, 8 ]
vertex  3 -> Algebra 1462    permutation [ 2, 5, 3, 8, 7, 1, 4, 6 ]
vertex  4 -> Algebra 1506    permutation [ 2, 3, 1, 7, 6, 5, 4, 8 ]
vertex  8 -> Algebra 1484    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]