Algebra 681

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  860    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1192    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1193    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 797

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  997    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1185    permutation [ 6, 1, 8, 2, 3, 4, 5, 7 ]

Algebra 860

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1370    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  877    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  681    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1371    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1372    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 877

Quiver

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

Relations

[ 7, 2, 1 ] 
[ 8, 2, 1 ] 
[ 5, 8, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 3, 5 ] 
[ 3, 5, 6 ] 
[ 2, 1, 7 ] 
[ 1, 7, 2 ] - [ 1, 8, 2 ] 
[ 5, 6, 3 ] - [ 5, 8, 3 ] 
[ 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 0 1 1)
(1 1 1 0 1 1 0 1)
(0 0 1 1 1 0 0 1)
(0 1 0 1 0 0 0 1)
(0 0 1 0 1 1 0 1)
(0 0 1 1 0 1 0 0)
(0 1 0 0 1 1 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1400    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  860    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1193    permutation [ 5, 1, 8, 7, 3, 4, 6, 2 ]
vertex  8 -> Algebra 1401    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 997

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  797    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1247    permutation [ 1, 3, 4, 5, 6, 7, 2, 8 ]

Algebra 1185

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra 1364    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  797    permutation [ 2, 4, 5, 6, 7, 1, 8, 3 ]
vertex  5 -> Algebra 1192    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1284    permutation [ 2, 8, 5, 6, 7, 1, 4, 3 ]

Algebra 1192

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra 1371    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1185    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  681    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1391    permutation [ 2, 8, 5, 6, 7, 1, 4, 3 ]

Algebra 1193

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1371    permutation [ 2, 1, 5, 6, 8, 7, 4, 3 ]
vertex  2 -> Algebra 1372    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1507    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  877    permutation [ 2, 8, 5, 6, 1, 7, 4, 3 ]
vertex  7 -> Algebra 1391    permutation [ 2, 8, 5, 6, 7, 1, 4, 3 ]
vertex  8 -> Algebra  681    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1216

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1515    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1244    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1507    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1244

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1520    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1216    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1247    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1401    permutation [ 2, 4, 8, 6, 1, 7, 3, 5 ]

Algebra 1247

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1364    permutation [ 5, 8, 7, 1, 2, 3, 4, 6 ]
vertex  5 -> Algebra 1244    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  997    permutation [ 1, 7, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1279    permutation [ 5, 2, 1, 7, 8, 3, 4, 6 ]

Algebra 1279

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1401    permutation [ 2, 7, 5, 1, 3, 4, 6, 8 ]
vertex  2 -> Algebra 1284    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1384    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1247    permutation [ 3, 2, 6, 7, 1, 8, 4, 5 ]

Algebra 1284

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1521    permutation [ 2, 3, 4, 5, 6, 7, 1, 8 ]
vertex  2 -> Algebra 1185    permutation [ 6, 1, 8, 7, 3, 4, 5, 2 ]
vertex  3 -> Algebra 1391    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1279    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]

Algebra 1364

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1520    permutation [ 4, 5, 6, 7, 8, 1, 3, 2 ]
vertex  2 -> Algebra 1384    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1185    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1247    permutation [ 4, 5, 6, 7, 1, 8, 3, 2 ]
vertex  5 -> Algebra 1371    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1521    permutation [ 8, 5, 6, 7, 1, 4, 3, 2 ]

Algebra 1370

Quiver

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

Relations

[ 5, 8, 1 ] 
[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 6, 2, 5 ] 
[ 2, 5, 6 ] 
[ 1, 5, 8 ] 
[ 5, 6, 2 ] - [ 5, 8, 2 ] 
[ 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 0 0 1)
(1 1 0 1 1 0 0 1)
(0 1 1 0 1 1 0 1)
(0 1 1 1 0 1 0 0)
(1 0 0 0 1 1 1 0)
(1 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  860    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1400    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1434    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1552    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1371

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1553    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1193    permutation [ 2, 1, 8, 7, 3, 4, 6, 5 ]
vertex  3 -> Algebra 1192    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1364    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  860    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1554    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1372

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1553    permutation [ 3, 1, 5, 6, 8, 7, 4, 2 ]
vertex  2 -> Algebra 1555    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1193    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1435    permutation [ 8, 5, 6, 1, 7, 4, 3, 2 ]
vertex  7 -> Algebra 1554    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  860    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1384

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1555    permutation [ 2, 8, 5, 1, 7, 3, 6, 4 ]
vertex  2 -> Algebra 1391    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  4 -> Algebra 1279    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1364    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  8 -> Algebra 1545    permutation [ 4, 7, 2, 1, 6, 8, 5, 3 ]

Algebra 1391

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1554    permutation [ 6, 8, 1, 7, 3, 4, 5, 2 ]
vertex  2 -> Algebra 1192    permutation [ 6, 1, 8, 7, 3, 4, 5, 2 ]
vertex  4 -> Algebra 1284    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1193    permutation [ 6, 1, 8, 7, 3, 4, 5, 2 ]
vertex  6 -> Algebra 1384    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  8 -> Algebra 1514    permutation [ 1, 6, 3, 5, 2, 7, 4, 8 ]

Algebra 1400

Quiver

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

Relations

[ 2, 5, 8, 1 ] 
[ 5, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 3, 5 ] 
[ 3, 5, 6 ] 
[ 1, 2, 5, 8 ] 
[ 5, 6, 3 ] - [ 5, 8, 3 ] 
[ 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 1 0 1 1 0 1)
(1 0 1 1 1 0 0 1)
(1 1 0 1 0 0 0 1)
(1 0 1 0 1 1 0 1)
(0 0 1 1 0 1 0 0)
(1 1 0 0 1 1 1 0)
(1 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  877    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1370    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1435    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1564    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1401

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1521    permutation [ 7, 5, 6, 3, 1, 2, 4, 8 ]
vertex  3 -> Algebra 1244    permutation [ 5, 1, 7, 2, 8, 4, 6, 3 ]
vertex  4 -> Algebra 1279    permutation [ 4, 1, 5, 6, 3, 7, 2, 8 ]
vertex  5 -> Algebra 1555    permutation [ 1, 8, 3, 4, 2, 6, 7, 5 ]
vertex  7 -> Algebra 1507    permutation [ 5, 1, 8, 7, 3, 4, 6, 2 ]
vertex  8 -> Algebra  877    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1434

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1435    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1553    permutation [ 7, 1, 2, 3, 4, 5, 6, 8 ]
vertex  7 -> Algebra 1370    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1543    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1435

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra 1434    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1372    permutation [ 4, 8, 7, 6, 2, 3, 5, 1 ]
vertex  7 -> Algebra 1400    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1545    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1507

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1557    permutation [ 6, 2, 7, 1, 5, 8, 4, 3 ]
vertex  2 -> Algebra 1520    permutation [ 8, 1, 7, 5, 2, 4, 6, 3 ]
vertex  3 -> Algebra 1193    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1401    permutation [ 2, 8, 5, 6, 1, 7, 4, 3 ]
vertex  5 -> Algebra 1216    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  7 -> Algebra 1514    permutation [ 2, 1, 5, 7, 8, 4, 6, 3 ]

Algebra 1514

Quiver

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

Relations

[ 3, 8, 1 ] 
[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 6, 1, 5 ] 
[ 1, 5, 6 ] 
[ 5, 8, 7 ] 
[ 2, 3, 8 ] 
[ 7, 5, 8 ] 
[ 5, 6, 1 ] - [ 5, 8, 1 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 1, 3 ] - [ 8, 2, 3 ] 
[ 8, 1, 5 ] - [ 8, 7, 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 0 1 1)
(0 1 0 1 0 0 0 0)
(1 1 1 0 1 1 0 1)
(1 0 1 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 1 0 1 0 1 1)

Good mutations

vertex  1 -> Algebra 1515    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  2 -> Algebra 1544    permutation [ 8, 6, 7, 1, 5, 2, 4, 3 ]
vertex  4 -> Algebra 1507    permutation [ 2, 1, 8, 6, 3, 7, 4, 5 ]
vertex  8 -> Algebra 1391    permutation [ 1, 5, 3, 7, 4, 2, 6, 8 ]

Algebra 1515

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1216    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1543    permutation [ 5, 6, 7, 8, 1, 2, 4, 3 ]
vertex  4 -> Algebra 1520    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1514    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  8 -> Algebra 1557    permutation [ 6, 2, 7, 1, 8, 3, 4, 5 ]

Algebra 1520

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1244    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1553    permutation [ 6, 8, 7, 1, 3, 2, 4, 5 ]
vertex  3 -> Algebra 1515    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1507    permutation [ 2, 5, 8, 6, 4, 7, 3, 1 ]
vertex  6 -> Algebra 1364    permutation [ 6, 8, 7, 1, 2, 3, 4, 5 ]
vertex  8 -> Algebra 1555    permutation [ 2, 5, 8, 6, 4, 7, 3, 1 ]

Algebra 1521

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1364    permutation [ 5, 8, 7, 6, 2, 3, 4, 1 ]
vertex  2 -> Algebra 1554    permutation [ 5, 8, 7, 6, 3, 2, 4, 1 ]
vertex  5 -> Algebra 1401    permutation [ 5, 6, 4, 7, 2, 3, 1, 8 ]
vertex  7 -> Algebra 1284    permutation [ 7, 1, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1564    permutation [ 8, 6, 4, 7, 2, 3, 1, 5 ]

Algebra 1543

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1544    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1434    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  6 -> Algebra 1515    permutation [ 5, 6, 8, 7, 1, 2, 3, 4 ]
vertex  7 -> Algebra 1552    permutation [ 6, 1, 2, 8, 3, 5, 7, 4 ]

Algebra 1544

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1545    permutation [ 3, 2, 1, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1543    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1514    permutation [ 4, 6, 8, 7, 5, 2, 3, 1 ]
vertex  7 -> Algebra 1567    permutation [ 3, 4, 8, 7, 6, 5, 2, 1 ]

Algebra 1545

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra 1544    permutation [ 3, 2, 1, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1435    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  6 -> Algebra 1384    permutation [ 4, 3, 8, 1, 7, 5, 2, 6 ]
vertex  7 -> Algebra 1564    permutation [ 6, 1, 2, 8, 3, 5, 7, 4 ]

Algebra 1552

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1553    permutation [ 3, 8, 5, 6, 1, 7, 4, 2 ]
vertex  2 -> Algebra 1567    permutation [ 5, 2, 4, 7, 1, 6, 3, 8 ]
vertex  7 -> Algebra 1543    permutation [ 2, 3, 5, 8, 6, 1, 7, 4 ]
vertex  8 -> Algebra 1370    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1553

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1371    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1372    permutation [ 2, 8, 1, 7, 3, 4, 6, 5 ]
vertex  5 -> Algebra 1552    permutation [ 5, 8, 1, 7, 3, 4, 6, 2 ]
vertex  6 -> Algebra 1520    permutation [ 4, 6, 5, 7, 8, 1, 3, 2 ]
vertex  7 -> Algebra 1434    permutation [ 2, 3, 4, 5, 6, 7, 1, 8 ]
vertex  8 -> Algebra 1557    permutation [ 3, 8, 5, 6, 7, 4, 1, 2 ]

Algebra 1554

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1555    permutation [ 1, 2, 7, 3, 4, 5, 8, 6 ]
vertex  2 -> Algebra 1557    permutation [ 4, 1, 6, 8, 3, 5, 7, 2 ]
vertex  3 -> Algebra 1391    permutation [ 3, 8, 5, 6, 7, 1, 4, 2 ]
vertex  6 -> Algebra 1521    permutation [ 8, 6, 5, 7, 1, 4, 3, 2 ]
vertex  7 -> Algebra 1372    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1371    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1555

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1554    permutation [ 1, 2, 4, 5, 6, 8, 3, 7 ]
vertex  2 -> Algebra 1372    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1520    permutation [ 8, 1, 7, 5, 2, 4, 6, 3 ]
vertex  4 -> Algebra 1384    permutation [ 4, 1, 6, 8, 3, 7, 5, 2 ]
vertex  7 -> Algebra 1557    permutation [ 4, 1, 6, 8, 3, 5, 7, 2 ]
vertex  8 -> Algebra 1401    permutation [ 1, 5, 3, 4, 8, 6, 7, 2 ]

Algebra 1557

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra 1553    permutation [ 7, 8, 1, 6, 3, 4, 5, 2 ]
vertex  3 -> Algebra 1567    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra 1507    permutation [ 4, 2, 8, 7, 5, 1, 3, 6 ]
vertex  5 -> Algebra 1515    permutation [ 4, 2, 6, 7, 8, 1, 3, 5 ]
vertex  7 -> Algebra 1555    permutation [ 2, 8, 5, 1, 6, 3, 7, 4 ]
vertex  8 -> Algebra 1554    permutation [ 2, 8, 5, 1, 6, 3, 7, 4 ]

Algebra 1564

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1521    permutation [ 7, 5, 6, 3, 8, 2, 4, 1 ]
vertex  5 -> Algebra 1567    permutation [ 2, 8, 4, 7, 1, 6, 3, 5 ]
vertex  7 -> Algebra 1545    permutation [ 2, 3, 5, 8, 6, 1, 7, 4 ]
vertex  8 -> Algebra 1400    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1567

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra 1552    permutation [ 5, 2, 7, 3, 1, 6, 4, 8 ]
vertex  4 -> Algebra 1544    permutation [ 8, 7, 1, 2, 6, 5, 4, 3 ]
vertex  5 -> Algebra 1557    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  8 -> Algebra 1564    permutation [ 5, 1, 7, 3, 8, 6, 4, 2 ]