Algebra 3
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
Cartan matrix
(1 0 1 1 1 1 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 1 1 1 1 1)
(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 0 0 0 0 0 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 18 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 22 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 23 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 4
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 1 1 1 1 1 1 1)
(0 1 1 1 1 1 1 1)
(0 1 1 0 0 0 0 0)
(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 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 24 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 28 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 11
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 1 1)
(1 1 1 0 0 0 0 0)
(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 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 4 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 51 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 55 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 18
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 3, 1, 8 ]
[ 1, 4, 3 ] - [ 1, 8, 3 ]
Cartan matrix
(1 0 1 1 1 1 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 0 0)
(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 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 24 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 3 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 82 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 22
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
Cartan matrix
(1 0 1 1 1 1 0 1)
(1 1 0 0 0 0 0 0)
(0 1 1 1 1 1 0 1)
(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 0 0 0 0 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 82 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 96 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 3 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 97 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 23
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
Cartan matrix
(1 0 1 1 1 1 1 0)
(1 1 0 0 0 0 0 0)
(0 1 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 0 0 0 0 0 1 0)
(0 1 1 1 1 1 1 1)
Good mutations
vertex 7 -> Algebra 97 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 3 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 24
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 2, 1, 8 ]
[ 1, 4, 2 ] - [ 1, 8, 2 ]
Cartan matrix
(1 1 1 1 1 1 1 1)
(1 1 1 0 0 0 0 0)
(0 0 1 0 0 0 0 0)
(0 1 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 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 4 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 18 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 103 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 28
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 1 1 1 1 1 0 1)
(0 1 1 1 1 1 0 1)
(0 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)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 55 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 103 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 117 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 4 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 51
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 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 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 176 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 179 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 180 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 55
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 0 1)
(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)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 28 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 179 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 193 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 82
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 3, 1, 8 ]
[ 1, 4, 3 ] - [ 1, 8, 3 ]
Cartan matrix
(1 0 1 1 1 1 0 1)
(1 1 1 0 0 0 0 0)
(1 0 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)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 103 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 22 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 269 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 18 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 94
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
Cartan matrix
(1 0 1 1 1 0 0 1)
(1 1 0 0 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 267 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 300 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 96 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 8 -> Algebra 301 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 96
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
Cartan matrix
(1 0 1 1 1 0 0 1)
(1 1 0 0 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 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 269 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 303 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 22 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 94 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 8 -> Algebra 304 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 97
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
Cartan matrix
(1 0 1 1 1 1 0 0)
(1 1 0 0 0 0 0 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)
(0 0 0 0 0 1 1 0)
(0 1 1 1 1 1 0 1)
Good mutations
vertex 6 -> Algebra 304 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 23 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 22 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 103
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 2, 1, 8 ]
[ 1, 4, 2 ] - [ 1, 8, 2 ]
Cartan matrix
(1 1 1 1 1 1 0 1)
(1 1 1 0 0 0 0 0)
(0 0 1 0 0 0 0 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 0 0 1 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 28 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 82 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 325 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 24 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 115
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 1 1 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(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 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 191 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 323 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 357 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 117 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 117
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 1 1 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(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 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 193 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 325 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 360 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 28 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 115 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 176
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 4 ], [ 3, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)
Good mutations
vertex 4 -> Algebra 51 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 304 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 478 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 303 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
Algebra 179
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 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 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 55 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 478 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 486 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 51 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 487 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 180
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 1 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 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 303 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 487 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 51 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 191
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 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 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 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 115 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 484 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 516 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 193 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 193
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 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 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 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 117 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 486 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 519 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 55 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 191 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 267
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 3, 1, 8 ]
[ 1, 4, 3 ] - [ 1, 8, 3 ]
Cartan matrix
(1 0 1 1 1 0 0 1)
(1 1 1 0 0 0 0 0)
(1 0 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 1 0)
(0 0 0 0 1 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 323 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 94 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 667 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 269 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 269
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 3, 1, 8 ]
[ 1, 4, 3 ] - [ 1, 8, 3 ]
Cartan matrix
(1 0 1 1 1 0 0 1)
(1 1 1 0 0 0 0 0)
(1 0 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 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 325 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 96 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 670 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 82 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 267 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 292
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
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 1 0)
(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 3 -> Algebra 659 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 719 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 298 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 720 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 298
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
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 1 0)
(0 0 0 0 0 1 0 0)
(0 0 0 1 0 0 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 665 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 728 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 300 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex 6 -> Algebra 292 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 729 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 300
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
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 0 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 3 -> Algebra 667 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 487 permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]
vertex 5 -> Algebra 94 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 303 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 7 -> Algebra 298 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex 8 -> Algebra 478 permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]
Algebra 301
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
Cartan matrix
(1 0 1 1 1 0 0 0)
(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 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 1 1 1 1 0 0 1)
Good mutations
vertex 5 -> Algebra 478 permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]
vertex 6 -> Algebra 304 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 8 -> Algebra 94 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 303
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
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 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 3 -> Algebra 670 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 180 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 96 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 300 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 8 -> Algebra 176 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
Algebra 304
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
Cartan matrix
(1 0 1 1 1 0 0 0)
(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 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 0 0 1)
Good mutations
vertex 5 -> Algebra 176 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 97 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 301 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 8 -> Algebra 96 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 323
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 2, 1, 8 ]
[ 1, 4, 2 ] - [ 1, 8, 2 ]
Cartan matrix
(1 1 1 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 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 115 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 267 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 773 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 325 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 325
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 2, 1, 8 ]
[ 1, 4, 2 ] - [ 1, 8, 2 ]
Cartan matrix
(1 1 1 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 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 117 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 269 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 776 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 103 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 323 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 349
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 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 1 0)
(0 0 1 1 0 1 1 0)
(0 0 1 1 0 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 508 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 765 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 355 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 355
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 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 1 0)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 514 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 771 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 357 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex 6 -> Algebra 349 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 357
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 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 0 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 516 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 773 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 115 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 360 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 7 -> Algebra 355 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
Algebra 360
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 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 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 519 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 776 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 117 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 357 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 478
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 4 ], [ 3, 1 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 1 0 0 0 1)
Good mutations
vertex 4 -> Algebra 179 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 301 permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]
vertex 6 -> Algebra 729 permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]
vertex 7 -> Algebra 176 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 300 permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]
Algebra 484
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 0 0)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 191 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 720 permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]
vertex 5 -> Algebra 988 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 486 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 8 -> Algebra 719 permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]
Algebra 486
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 0 0)
(0 0 0 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 0 0 1)
Good mutations
vertex 2 -> Algebra 193 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 729 permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]
vertex 5 -> Algebra 989 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 179 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 484 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 8 -> Algebra 728 permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]
Algebra 487
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 1 0 1)
(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 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 300 permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]
vertex 6 -> Algebra 728 permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]
vertex 7 -> Algebra 180 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 179 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 508
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 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 1 0)
(0 0 1 1 0 1 1 0)
(0 0 1 1 0 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 349 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 985 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 514 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 514
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 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 1 0)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 355 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 987 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 516 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex 6 -> Algebra 508 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 516
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 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 0 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 357 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 988 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 191 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 519 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 7 -> Algebra 514 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
Algebra 519
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 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 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 360 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 989 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 193 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 516 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 659
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 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 1 0)
(0 0 1 1 0 1 1 0)
(0 0 1 1 0 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 765 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 292 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 665 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 665
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 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 1 0)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 771 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 298 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 667 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex 6 -> Algebra 659 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 667
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 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 0 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 2 -> Algebra 773 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 300 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 267 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 670 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 7 -> Algebra 665 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
Algebra 670
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 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 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 2 -> Algebra 776 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 303 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 269 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 667 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 692
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 7, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
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 1 1)
(0 1 1 0 1 1 1 1)
(0 1 1 0 0 1 1 1)
(0 1 1 0 0 0 1 1)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 711 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 8 -> Algebra 985 permutation [ 1, 3, 2, 7, 4, 5, 6, 8 ]
Algebra 711
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 6, 7 ], [ 7, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
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 1 1)
(0 0 0 0 1 0 0 0)
(0 1 1 0 0 1 1 1)
(0 1 1 0 0 0 1 1)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 717 permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex 5 -> Algebra 692 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 8 -> Algebra 987 permutation [ 1, 3, 2, 7, 4, 5, 6, 8 ]
Algebra 717
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 8 ], [ 4, 6 ], [ 4, 7 ], [ 5, 6 ], [ 7, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
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 0 1 1 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 1 1 0 0 0 1 1)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 719 permutation [ 1, 2, 3, 7, 5, 6, 4, 8 ]
vertex 5 -> Algebra 726 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 711 permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex 8 -> Algebra 988 permutation [ 1, 3, 2, 7, 4, 5, 6, 8 ]
Algebra 719
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 7 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
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 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 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 292 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 728 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 7 -> Algebra 717 permutation [ 1, 2, 3, 7, 5, 6, 4, 8 ]
vertex 8 -> Algebra 484 permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]
Algebra 720
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
Cartan matrix
(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 1 1 1 1 0)
(0 0 0 1 0 1 1 0)
(0 0 0 1 0 0 1 0)
(0 1 1 1 0 0 0 1)
Good mutations
vertex 4 -> Algebra 484 permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]
vertex 5 -> Algebra 729 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 292 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 726
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 8 ], [ 4, 5 ], [ 4, 7 ], [ 5, 6 ], [ 7, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
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 1 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 1 1 0 0 0 1 1)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 728 permutation [ 1, 2, 3, 7, 5, 6, 4, 8 ]
vertex 6 -> Algebra 717 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 989 permutation [ 1, 3, 2, 7, 4, 5, 6, 8 ]
Algebra 728
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 7 ], [ 5, 6 ], [ 5, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
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 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 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 298 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 487 permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]
vertex 6 -> Algebra 719 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 7 -> Algebra 726 permutation [ 1, 2, 3, 7, 5, 6, 4, 8 ]
vertex 8 -> Algebra 486 permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]
Algebra 729
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
Cartan matrix
(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 1 1 1 1 0)
(0 0 0 0 0 1 0 0)
(0 0 0 1 0 0 1 0)
(0 1 1 1 0 0 0 1)
Good mutations
vertex 4 -> Algebra 486 permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]
vertex 5 -> Algebra 478 permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]
vertex 6 -> Algebra 720 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 298 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 765
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 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 1 0)
(0 1 1 1 0 1 1 0)
(0 1 1 1 0 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 349 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 659 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 771 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 771
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 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 1 0)
(0 0 0 0 0 1 0 0)
(0 1 1 1 0 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 355 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 665 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 773 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex 6 -> Algebra 765 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 773
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 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 0 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 357 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 667 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 323 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 776 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 7 -> Algebra 771 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
Algebra 776
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 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 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 360 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 670 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 325 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 773 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
Algebra 985
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 1 0)
(0 1 1 1 0 1 1 0)
(0 1 1 1 0 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 508 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 987 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 692 permutation [ 1, 3, 2, 5, 6, 7, 4, 8 ]
Algebra 987
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 1 0)
(0 0 0 0 0 1 0 0)
(0 1 1 1 0 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 514 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 988 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex 6 -> Algebra 985 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 711 permutation [ 1, 3, 2, 5, 6, 7, 4, 8 ]
Algebra 988
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 0 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 516 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 484 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 989 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 7 -> Algebra 987 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex 8 -> Algebra 717 permutation [ 1, 3, 2, 5, 6, 7, 4, 8 ]
Algebra 989
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
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 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 519 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 486 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 988 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 8 -> Algebra 726 permutation [ 1, 3, 2, 5, 6, 7, 4, 8 ]