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 ]