Algebra 175

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  251    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  475    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 251

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  175    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  631    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 257

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  313    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  644    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  646    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 313

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  257    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  750    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  752    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 475

Quiver

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

Relations

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

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 1 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 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  631    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  644    permutation [ 4, 1, 2, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  175    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 631

Quiver

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

Relations

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

Cartan matrix

(1 1 1 0 0 0 0 0)
(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 1 0 0)
(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  2 -> Algebra  475    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  750    permutation [ 4, 1, 2, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  251    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 644

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  750    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  257    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  475    permutation [ 2, 3, 4, 1, 5, 6, 7, 8 ]
vertex  7 -> Algebra  929    permutation [ 2, 3, 8, 1, 7, 6, 5, 4 ]

Algebra 646

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  752    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  929    permutation [ 2, 3, 8, 1, 7, 6, 5, 4 ]
vertex  6 -> Algebra  922    permutation [ 2, 3, 8, 6, 7, 5, 1, 4 ]
vertex  7 -> Algebra  257    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 750

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  644    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  313    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  631    permutation [ 2, 3, 4, 1, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1107    permutation [ 3, 2, 8, 1, 7, 6, 5, 4 ]

Algebra 752

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  646    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1107    permutation [ 3, 2, 8, 1, 7, 6, 5, 4 ]
vertex  6 -> Algebra 1098    permutation [ 3, 2, 8, 6, 7, 5, 1, 4 ]
vertex  7 -> Algebra  313    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 897

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1072    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  922    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]

Algebra 922

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1098    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  646    permutation [ 7, 1, 2, 8, 6, 4, 5, 3 ]
vertex  5 -> Algebra  897    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]

Algebra 929

Quiver

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

Relations

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

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 0 0 0 0 1)
(0 1 1 1 0 0 1 1)
(0 0 0 1 0 0 1 1)
(0 0 0 0 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  1 -> Algebra 1107    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  644    permutation [ 4, 1, 2, 8, 7, 6, 5, 3 ]
vertex  7 -> Algebra  646    permutation [ 4, 1, 2, 8, 7, 6, 5, 3 ]

Algebra 1072

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  897    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1098    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]

Algebra 1098

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  922    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  752    permutation [ 7, 2, 1, 8, 6, 4, 5, 3 ]
vertex  5 -> Algebra 1072    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]

Algebra 1107

Quiver

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

Relations

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

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 0 0 0 0 1)
(1 1 1 1 0 0 1 1)
(0 0 0 1 0 0 1 1)
(0 0 0 0 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  1 -> Algebra  929    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  750    permutation [ 4, 2, 1, 8, 7, 6, 5, 3 ]
vertex  7 -> Algebra  752    permutation [ 4, 2, 1, 8, 7, 6, 5, 3 ]