Algebra 19

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra   85    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   87    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   88    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 20

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra   80    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra   89    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra   90    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   91    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   92    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 21

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra   81    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra   93    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   95    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 26

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   53    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  101    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  111    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  112    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 27

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   54    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  102    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  114    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 53

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   26    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  177    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  187    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  188    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 54

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   27    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  178    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  190    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 80

Quiver

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

Relations

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

Cartan matrix

(1 0 1 1 0 1 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 0 0)
(0 0 1 1 0 1 1 0)
(0 0 1 1 1 0 0 0)
(0 0 0 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  101    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  263    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  264    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 81

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  102    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   21    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  266    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 85

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   89    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra   19    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  278    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  279    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  280    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 87

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  279    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  284    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   19    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  285    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 88

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  280    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  285    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   19    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 89

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra   85    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  288    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  289    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  290    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 90

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  263    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  291    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra   93    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  293    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 91

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  264    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  289    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  294    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  295    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 92

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  290    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  293    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  295    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 93

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  266    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  297    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra   21    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra   90    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  299    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 95

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  299    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   21    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 101

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   26    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   80    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  319    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  320    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 102

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   27    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   81    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  322    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 111

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  187    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  319    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  114    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra   26    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 112

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  188    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  320    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  351    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   26    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 114

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  190    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  322    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra   27    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  111    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 177

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   53    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  479    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  480    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  481    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  482    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 178

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   54    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  477    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  483    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  485    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 187

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  111    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  480    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  190    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra   53    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 188

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  112    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  481    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  510    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   53    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 190

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  114    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  483    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra   54    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  187    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 263

Quiver

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

Relations

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

Cartan matrix

(1 0 1 1 0 0 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 0 0)
(0 0 1 1 0 0 1 0)
(0 0 1 1 1 1 0 0)
(0 0 1 1 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  319    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   90    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  266    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra   80    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 264

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  320    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   91    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  661    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   80    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 266

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  322    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   93    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra   81    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  263    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 278

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  288    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra   85    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  693    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 279

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  289    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra   87    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  694    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   85    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  695    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 280

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  290    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra   88    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  693    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  695    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   85    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 282

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  700    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  284    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  701    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 284

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  482    permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra   87    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  282    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  479    permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]

Algebra 285

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  695    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  479    permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra   88    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   87    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 288

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  291    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra  278    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra   89    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  712    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 289

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   91    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  279    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  713    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   89    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  714    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 290

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   92    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  280    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  712    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  714    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   89    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 291

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   90    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  297    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  288    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  8 -> Algebra  718    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 293

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  718    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  299    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra   92    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   90    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 294

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  661    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  485    permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra   91    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  477    permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]

Algebra 295

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  714    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  477    permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra   92    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   91    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 297

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   93    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  291    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  727    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 299

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  727    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra   95    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  293    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra   93    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 319

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  111    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  263    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  322    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  101    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 320

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  112    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  264    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  767    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  101    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 322

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  114    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  266    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  102    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  319    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 351

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  510    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  767    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  112    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 477

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  178    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  295    permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  294    permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]

Algebra 479

Quiver

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

Relations

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

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 1 1 0 0 0 0)
(1 0 1 0 0 0 0 0)
(0 0 0 1 1 0 0 0)
(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  4 -> Algebra  177    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  285    permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  701    permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex  8 -> Algebra  284    permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]

Algebra 480

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  187    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  695    permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]
vertex  5 -> Algebra  483    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  177    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  694    permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]

Algebra 481

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  188    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  701    permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex  6 -> Algebra  986    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  177    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  700    permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]

Algebra 482

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  284    permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  694    permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]
vertex  7 -> Algebra  700    permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex  8 -> Algebra  177    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 483

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  190    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  714    permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]
vertex  5 -> Algebra  178    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  480    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  713    permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]

Algebra 485

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  294    permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]
vertex  5 -> Algebra  713    permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]
vertex  8 -> Algebra  178    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 510

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  351    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  986    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  188    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 661

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  767    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  294    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  264    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 693

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  712    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  280    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  278    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 694

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  713    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  482    permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]
vertex  6 -> Algebra  279    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  480    permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]

Algebra 695

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  714    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  285    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  480    permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]
vertex  7 -> Algebra  280    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  279    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 698

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  700    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  8 -> Algebra  986    permutation [ 1, 3, 2, 7, 4, 5, 6, 8 ]

Algebra 700

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  282    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  482    permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex  7 -> Algebra  698    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  8 -> Algebra  481    permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]

Algebra 701

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  481    permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex  6 -> Algebra  479    permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex  8 -> Algebra  282    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 712

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  718    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra  693    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  290    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  288    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 713

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  485    permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]
vertex  5 -> Algebra  694    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  289    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  483    permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]

Algebra 714

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  295    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  695    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  483    permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]
vertex  7 -> Algebra  290    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  289    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 718

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  293    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  727    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  712    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  8 -> Algebra  291    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 727

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  299    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  718    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  297    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 767

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  351    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  661    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  320    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 986

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  510    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  481    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  698    permutation [ 1, 3, 2, 5, 6, 7, 4, 8 ]