E8_15.html

Algebra 805

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1004    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1184    permutation [ 7, 1, 8, 2, 3, 4, 6, 5 ]
vertex  3 -> Algebra  879    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  809    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 809

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1008    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1127    permutation [ 1, 8, 2, 3, 4, 6, 7, 5 ]
vertex  3 -> Algebra  882    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  805    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 873

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1050    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  894    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra  882    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 879

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1056    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  805    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  882    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 882

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1059    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  809    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  873    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  879    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 892

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1066    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  919    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  894    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 894

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1068    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  920    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  873    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra  892    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 919

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1093    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  892    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  920    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 920

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1094    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  894    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  919    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1004

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  805    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1056    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1008    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1008

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  809    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1059    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1004    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1050

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  873    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1068    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra 1059    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 1056

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  879    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1004    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1059    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1059

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  882    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1008    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1050    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1056    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1066

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  892    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1274    permutation [ 6, 8, 1, 2, 3, 4, 5, 7 ]
vertex  4 -> Algebra 1093    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1068    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1068

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  894    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1094    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1050    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra 1066    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1093

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  919    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1276    permutation [ 6, 8, 1, 2, 3, 4, 5, 7 ]
vertex  5 -> Algebra 1066    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1094    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1094

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  920    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1068    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra 1093    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1127

Quiver

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

Relations

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

Cartan matrix

(1 1 0 1 1 0 0 0)
(0 1 1 1 1 0 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 1 1 0 0 1)
(0 1 0 0 1 0 0 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  3 -> Algebra  809    permutation [ 1, 3, 4, 5, 8, 6, 7, 2 ]
vertex  7 -> Algebra 1184    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1276    permutation [ 1, 8, 4, 5, 3, 6, 7, 2 ]

Algebra 1184

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  805    permutation [ 2, 4, 5, 6, 8, 7, 1, 3 ]
vertex  7 -> Algebra 1127    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1274    permutation [ 2, 8, 5, 6, 4, 7, 1, 3 ]

Algebra 1274

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra 1184    permutation [ 7, 1, 8, 5, 3, 4, 6, 2 ]
vertex  4 -> Algebra 1066    permutation [ 3, 4, 5, 6, 7, 1, 8, 2 ]
vertex  6 -> Algebra 1276    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1276

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra 1127    permutation [ 1, 8, 5, 3, 4, 6, 7, 2 ]
vertex  4 -> Algebra 1093    permutation [ 3, 4, 5, 6, 7, 1, 8, 2 ]
vertex  7 -> Algebra 1274    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]