Algebra 22
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 5, 3, 4, 2 ]
[ 4, 2, 5, 3 ]
[ 2, 5, 3, 4 ]
[ 3, 4, 2, 5 ]
Cartan matrix
(1 1 1 0 1 1 1)
(0 1 1 0 1 1 1)
(0 1 1 1 0 0 0)
(0 1 0 1 1 1 1)
(0 0 1 1 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 42 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 81 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 82 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 84 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 23
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 6 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 4, 3, 5, 2 ]
[ 6, 5, 2 ]
[ 5, 2, 4, 3 ]
[ 3, 5, 2, 4 ]
[ 5, 2, 6 ]
[ 2, 4, 3, 5 ] - [ 2, 6, 5 ]
Cartan matrix
(1 1 1 1 1 1 1)
(0 1 1 1 1 1 1)
(0 1 1 0 1 0 0)
(0 0 1 1 1 0 0)
(0 1 0 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 43 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 85 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 30 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 82 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 87 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 30
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 4, 3, 2 ]
[ 6, 3, 2 ]
[ 5, 4, 3 ]
[ 4, 3, 5 ]
[ 3, 2, 6 ]
[ 2, 4, 3 ] - [ 2, 6, 3 ]
[ 3, 2, 4 ] - [ 3, 5, 4 ]
Cartan matrix
(1 1 1 1 0 1 1)
(0 1 1 1 0 1 1)
(0 1 1 1 1 0 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 50 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 102 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 23 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 103 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 104 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 42
Quiver
[ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 5, 3, 4, 2 ]
[ 4, 2, 5, 3 ]
[ 2, 5, 3, 4 ]
[ 3, 4, 2, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 1 1)
(1 1 1 1 0 0 0)
(1 1 0 1 1 1 1)
(0 0 1 1 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 22 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 128 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 129 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 131 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 43
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 6 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 4, 3, 5, 2 ]
[ 6, 5, 2 ]
[ 5, 2, 4, 3 ]
[ 3, 5, 2, 4 ]
[ 5, 2, 6 ]
[ 2, 4, 3, 5 ] - [ 2, 6, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 1 1 1)
(1 1 1 0 1 0 0)
(0 0 1 1 1 0 0)
(1 1 0 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 23 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 132 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 50 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 129 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 134 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 50
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 4, 3, 2 ]
[ 6, 3, 2 ]
[ 5, 4, 3 ]
[ 4, 3, 5 ]
[ 3, 2, 6 ]
[ 2, 4, 3 ] - [ 2, 6, 3 ]
[ 3, 2, 4 ] - [ 3, 5, 4 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 1 1)
(1 1 1 1 1 0 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 30 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 148 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 149 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 43 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 150 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 151 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 62
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 5, 3, 4, 1 ]
[ 4, 1, 5, 3 ]
[ 1, 5, 3, 4 ]
[ 3, 4, 1, 5 ]
Cartan matrix
(1 0 1 0 1 1 1)
(1 1 1 1 0 0 0)
(1 0 1 1 0 0 0)
(1 0 0 1 1 1 1)
(0 0 1 1 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 77 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 66 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 108 permutation [ 2, 3, 1, 5, 6, 7, 4 ]
vertex 7 -> Algebra 177 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 63
Quiver
[ 1, 4 ], [ 1, 6 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 4, 3, 5, 1 ]
[ 6, 5, 1 ]
[ 5, 1, 4, 3 ]
[ 3, 5, 1, 4 ]
[ 5, 1, 6 ]
[ 1, 4, 3, 5 ] - [ 1, 6, 5 ]
Cartan matrix
(1 0 1 1 1 1 1)
(1 1 1 0 1 0 0)
(1 0 1 0 1 0 0)
(0 0 1 1 1 0 0)
(1 0 0 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 78 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 108 permutation [ 2, 3, 1, 5, 6, 7, 4 ]
vertex 7 -> Algebra 180 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 66
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 5, 3, 1 ]
[ 3, 4, 2 ]
[ 1, 5, 3 ]
[ 2, 3, 4 ]
[ 5, 3, 4 ]
[ 4, 2, 3 ] - [ 4, 5, 3 ]
[ 3, 1, 5 ] - [ 3, 4, 5 ]
Cartan matrix
(1 0 0 0 1 1 1)
(1 1 1 0 0 0 0)
(1 0 1 1 1 1 1)
(0 1 1 1 1 1 1)
(0 0 1 0 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 184 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 91 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 62 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 7 -> Algebra 187 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 77
Quiver
[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 5, 2, 4, 1 ]
[ 4, 1, 5, 2 ]
[ 1, 5, 2, 4 ]
[ 2, 4, 1, 5 ]
Cartan matrix
(1 1 1 0 1 1 1)
(1 1 1 1 0 0 0)
(0 0 1 0 0 0 0)
(1 0 0 1 1 1 1)
(0 1 1 1 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 81 permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex 3 -> Algebra 62 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 5 -> Algebra 155 permutation [ 3, 2, 1, 5, 6, 7, 4 ]
vertex 7 -> Algebra 209 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 78
Quiver
[ 1, 4 ], [ 1, 6 ], [ 2, 3 ], [ 2, 5 ], [ 4, 2 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 4, 2, 5, 1 ]
[ 6, 5, 1 ]
[ 5, 1, 4, 2 ]
[ 2, 5, 1, 4 ]
[ 5, 1, 6 ]
[ 1, 4, 2, 5 ] - [ 1, 6, 5 ]
Cartan matrix
(1 1 1 1 1 1 1)
(1 1 1 0 1 0 0)
(0 0 1 0 0 0 0)
(0 1 1 1 1 0 0)
(1 0 0 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 85 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 3 -> Algebra 63 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 155 permutation [ 3, 2, 1, 5, 6, 7, 4 ]
vertex 7 -> Algebra 212 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 81
Quiver
[ 1, 5 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 5, 2, 1 ]
[ 1, 5, 2 ]
[ 4, 5, 2 ]
[ 4, 5, 3 ]
[ 3, 4, 5 ]
[ 5, 2, 4 ] - [ 5, 3, 4 ]
[ 2, 1, 5 ] - [ 2, 4, 5 ]
Cartan matrix
(1 0 1 0 1 1 1)
(1 1 0 1 1 1 1)
(0 0 1 1 0 0 0)
(0 0 0 1 1 1 1)
(0 1 1 1 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 216 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 22 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 91 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 4 -> Algebra 77 permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex 5 -> Algebra 217 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 219 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 82
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 2 ]
[ 4, 2, 3 ]
[ 5, 2, 3 ]
[ 2, 3, 4 ]
[ 5, 2, 6 ]
[ 3, 4, 2 ] - [ 3, 5, 2 ]
[ 2, 3, 5 ] - [ 2, 6, 5 ]
Cartan matrix
(1 1 1 0 1 1 1)
(0 1 1 0 1 1 1)
(0 1 1 1 1 0 0)
(0 1 0 1 0 1 1)
(0 1 0 0 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 129 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 220 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 221 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 23 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 22 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 223 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 84
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 5, 3, 4, 2 ]
[ 4, 2, 5, 3 ]
[ 2, 5, 3, 4 ]
[ 3, 4, 2, 5 ]
Cartan matrix
(1 1 1 0 1 1 0)
(0 1 1 0 1 1 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 1 0)
(0 0 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 131 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 219 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 223 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 226 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 22 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 85
Quiver
[ 1, 4 ], [ 1, 6 ], [ 2, 1 ], [ 2, 5 ], [ 3, 5 ], [ 4, 2 ], [ 4, 3 ], [ 5, 4 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 4, 2, 1 ]
[ 6, 2, 1 ]
[ 5, 4, 2 ]
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 2, 1, 6 ]
[ 1, 4, 2 ] - [ 1, 6, 2 ]
[ 2, 1, 4 ] - [ 2, 5, 4 ]
[ 4, 2, 5 ] - [ 4, 3, 5 ]
Cartan matrix
(1 1 1 1 1 1 1)
(1 1 0 1 1 0 0)
(0 0 1 0 1 0 0)
(0 1 1 1 1 0 0)
(0 0 0 1 1 0 0)
(0 1 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 227 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 23 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 228 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 78 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 7 -> Algebra 230 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 87
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 6 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 4, 3, 5, 2 ]
[ 6, 5, 2 ]
[ 5, 2, 4, 3 ]
[ 3, 5, 2, 4 ]
[ 5, 2, 6 ]
[ 2, 4, 3, 5 ] - [ 2, 6, 5 ]
Cartan matrix
(1 1 1 1 1 1 0)
(0 1 1 1 1 1 0)
(0 1 1 0 1 0 0)
(0 0 1 1 1 0 0)
(0 1 0 1 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 134 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 230 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 104 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 223 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 23 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 91
Quiver
[ 1, 5 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 5, 2, 1 ]
[ 1, 5, 2 ]
[ 3, 4, 5, 2 ]
[ 4, 5, 2, 3 ]
[ 5, 2, 3, 4 ]
[ 2, 1, 5 ] - [ 2, 3, 4, 5 ]
Cartan matrix
(1 0 0 0 1 1 1)
(1 1 1 1 1 1 1)
(0 0 1 1 1 1 1)
(0 1 0 1 1 1 1)
(0 1 1 0 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 66 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 81 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 238 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 240 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 102
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 6, 3, 4, 2 ]
[ 4, 2, 6, 3 ]
[ 2, 6, 3, 4 ]
[ 3, 4, 2, 6 ]
Cartan matrix
(1 1 1 0 0 1 1)
(0 1 1 0 0 1 1)
(0 1 1 1 1 0 0)
(0 1 0 1 1 1 1)
(0 0 0 0 1 0 0)
(0 0 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 149 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 220 permutation [ 2, 6, 1, 3, 7, 4, 5 ]
vertex 4 -> Algebra 30 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 221 permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex 6 -> Algebra 255 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 256 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 103
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 7 ], [ 3, 5 ], [ 3, 6 ], [ 4, 3 ], [ 5, 4 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 4, 3, 6, 2 ]
[ 7, 6, 2 ]
[ 5, 4, 3 ]
[ 6, 2, 4, 3 ]
[ 4, 3, 5 ]
[ 6, 2, 7 ]
[ 3, 5, 4 ] - [ 3, 6, 2, 4 ]
[ 2, 4, 3, 6 ] - [ 2, 7, 6 ]
Cartan matrix
(1 1 1 1 0 1 1)
(0 1 1 1 0 1 1)
(0 1 1 1 1 1 0)
(0 0 1 1 0 1 0)
(0 0 0 1 1 0 0)
(0 1 0 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 150 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 105 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 4 -> Algebra 255 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 30 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 104
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 4, 3, 2 ]
[ 6, 3, 2 ]
[ 5, 4, 3 ]
[ 4, 3, 5 ]
[ 3, 2, 6 ]
[ 2, 4, 3 ] - [ 2, 6, 3 ]
[ 3, 2, 4 ] - [ 3, 5, 4 ]
Cartan matrix
(1 1 1 1 0 1 0)
(0 1 1 1 0 1 0)
(0 1 1 1 1 0 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 0 0)
(0 0 1 0 1 1 0)
(0 0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 151 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 256 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 87 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 7 -> Algebra 30 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 105
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 7 ], [ 3, 2 ], [ 3, 6 ], [ 4, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 3 ]
Relations
[ 4, 3, 2 ]
[ 7, 3, 2 ]
[ 6, 4, 3 ]
[ 4, 3, 6 ]
[ 3, 2, 7 ]
[ 2, 4, 3 ] - [ 2, 7, 3 ]
[ 3, 2, 4 ] - [ 3, 6, 4 ]
Cartan matrix
(1 1 1 1 0 0 1)
(0 1 1 1 0 0 1)
(0 1 1 1 0 1 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 1 0)
(0 0 0 1 0 1 0)
(0 0 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 152 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 177 permutation [ 3, 1, 2, 7, 4, 6, 5 ]
vertex 5 -> Algebra 108 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 103 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 7 -> Algebra 180 permutation [ 3, 1, 2, 7, 4, 6, 5 ]
Algebra 108
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 7 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 7, 3 ]
Relations
[ 4, 3, 2 ]
[ 7, 3, 2 ]
[ 5, 4, 3 ]
[ 4, 3, 5 ]
[ 3, 2, 7 ]
[ 2, 4, 3 ] - [ 2, 7, 3 ]
[ 3, 2, 4 ] - [ 3, 5, 4 ]
Cartan matrix
(1 1 1 1 0 0 1)
(0 1 1 1 0 0 1)
(0 1 1 1 1 1 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 155 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 62 permutation [ 3, 1, 2, 7, 4, 5, 6 ]
vertex 6 -> Algebra 105 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 63 permutation [ 3, 1, 2, 7, 4, 5, 6 ]
Algebra 128
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 2, 4, 1 ]
[ 4, 5, 3 ]
[ 1, 2, 4 ]
[ 2, 4, 5 ]
[ 3, 4, 5 ]
[ 4, 1, 2 ] - [ 4, 5, 2 ]
[ 5, 2, 4 ] - [ 5, 3, 4 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 1 0 0 0)
(1 0 1 1 0 0 0)
(1 1 0 1 1 1 1)
(0 1 1 1 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 216 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 42 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 138 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 276 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 278 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 129
Quiver
[ 2, 1 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 2 ]
[ 4, 2, 3 ]
[ 5, 2, 3 ]
[ 2, 3, 4 ]
[ 5, 2, 6 ]
[ 3, 4, 2 ] - [ 3, 5, 2 ]
[ 2, 3, 5 ] - [ 2, 6, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 1 1)
(1 1 1 1 1 0 0)
(1 1 0 1 0 1 1)
(1 1 0 0 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 82 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 255 permutation [ 3, 2, 4, 6, 7, 1, 5 ]
vertex 3 -> Algebra 279 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 43 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 42 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 281 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 131
Quiver
[ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 5, 3, 4, 2 ]
[ 4, 2, 5, 3 ]
[ 2, 5, 3, 4 ]
[ 3, 4, 2, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 1 0)
(1 1 1 1 0 0 0)
(1 1 0 1 1 1 0)
(0 0 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 84 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 278 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 281 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 284 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 42 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 132
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 4, 2 ], [ 4, 3 ], [ 5, 1 ], [ 5, 4 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 2, 5, 1 ]
[ 5, 4, 3 ]
[ 2, 5, 4 ]
[ 3, 5, 4 ]
[ 1, 2, 5 ]
[ 5, 1, 2 ] - [ 5, 4, 2 ]
[ 4, 2, 5 ] - [ 4, 3, 5 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 1 0 0)
(1 0 1 0 1 0 0)
(0 1 1 1 1 0 0)
(1 1 0 1 1 0 0)
(0 1 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 227 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 43 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 148 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 285 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 187 permutation [ 1, 3, 5, 4, 2, 6, 7 ]
vertex 7 -> Algebra 286 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 134
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 6 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 4, 3, 5, 2 ]
[ 6, 5, 2 ]
[ 5, 2, 4, 3 ]
[ 3, 5, 2, 4 ]
[ 5, 2, 6 ]
[ 2, 4, 3, 5 ] - [ 2, 6, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 1 1 0)
(1 1 1 0 1 0 0)
(0 0 1 1 1 0 0)
(1 1 0 1 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 87 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 286 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 151 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 281 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 43 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 138
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 2, 3, 1 ]
[ 1, 2, 3 ]
[ 4, 5, 2, 3 ]
[ 5, 2, 3, 4 ]
[ 2, 3, 4, 5 ]
[ 3, 1, 2 ] - [ 3, 4, 5, 2 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 1 1 0 0 0)
(1 1 1 1 1 1 1)
(0 1 0 1 1 1 1)
(0 1 1 0 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 128 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 293 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 295 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 148
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 2 ], [ 5, 4 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 2, 3, 1 ]
[ 1, 2, 3 ]
[ 5, 4, 2, 3 ]
[ 2, 3, 5, 4 ]
[ 4, 2, 3, 5 ]
[ 3, 1, 2 ] - [ 3, 5, 4, 2 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 1 0 1 0 0)
(1 1 1 1 1 0 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 0 0)
(0 1 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 50 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 307 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 132 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 240 permutation [ 1, 3, 5, 4, 2, 6, 7 ]
vertex 7 -> Algebra 308 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 149
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 6, 3, 4, 2 ]
[ 4, 2, 6, 3 ]
[ 2, 6, 3, 4 ]
[ 3, 4, 2, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 0 1 1)
(1 1 1 1 1 0 0)
(1 1 0 1 1 1 1)
(0 0 0 0 1 0 0)
(0 0 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 102 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 309 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 50 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 279 permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex 6 -> Algebra 310 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 311 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 150
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 7 ], [ 3, 5 ], [ 3, 6 ], [ 4, 3 ], [ 5, 4 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 4, 3, 6, 2 ]
[ 7, 6, 2 ]
[ 5, 4, 3 ]
[ 6, 2, 4, 3 ]
[ 4, 3, 5 ]
[ 6, 2, 7 ]
[ 3, 5, 4 ] - [ 3, 6, 2, 4 ]
[ 2, 4, 3, 6 ] - [ 2, 7, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 1 1)
(1 1 1 1 1 1 0)
(0 0 1 1 0 1 0)
(0 0 0 1 1 0 0)
(1 1 0 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 103 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 312 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 152 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 4 -> Algebra 310 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 50 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 151
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 4, 3, 2 ]
[ 6, 3, 2 ]
[ 5, 4, 3 ]
[ 4, 3, 5 ]
[ 3, 2, 6 ]
[ 2, 4, 3 ] - [ 2, 6, 3 ]
[ 3, 2, 4 ] - [ 3, 5, 4 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 1 0)
(1 1 1 1 1 0 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 0 0)
(0 0 1 0 1 1 0)
(0 0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 104 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 308 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 311 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 134 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 7 -> Algebra 50 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 152
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 7 ], [ 3, 2 ], [ 3, 6 ], [ 4, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 3 ]
Relations
[ 4, 3, 2 ]
[ 7, 3, 2 ]
[ 6, 4, 3 ]
[ 4, 3, 6 ]
[ 3, 2, 7 ]
[ 2, 4, 3 ] - [ 2, 7, 3 ]
[ 3, 2, 4 ] - [ 3, 6, 4 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 0 1)
(1 1 1 1 0 1 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 1 0)
(0 0 0 1 0 1 0)
(0 0 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 105 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 315 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 209 permutation [ 3, 2, 1, 7, 4, 6, 5 ]
vertex 5 -> Algebra 155 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 150 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 7 -> Algebra 212 permutation [ 3, 2, 1, 7, 4, 6, 5 ]
Algebra 155
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 7 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 7, 3 ]
Relations
[ 4, 3, 2 ]
[ 7, 3, 2 ]
[ 5, 4, 3 ]
[ 4, 3, 5 ]
[ 3, 2, 7 ]
[ 2, 4, 3 ] - [ 2, 7, 3 ]
[ 3, 2, 4 ] - [ 3, 5, 4 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 0 1)
(1 1 1 1 1 1 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 108 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 318 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 77 permutation [ 3, 2, 1, 7, 4, 5, 6 ]
vertex 6 -> Algebra 152 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 78 permutation [ 3, 2, 1, 7, 4, 5, 6 ]
Algebra 177
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 5, 3, 4, 1 ]
[ 4, 1, 5, 3 ]
[ 1, 5, 3, 4 ]
[ 3, 4, 1, 5 ]
Cartan matrix
(1 0 1 0 1 1 0)
(1 1 1 1 0 0 0)
(1 0 1 1 0 0 0)
(1 0 0 1 1 1 0)
(0 0 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 209 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 187 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 105 permutation [ 2, 3, 1, 5, 7, 6, 4 ]
vertex 6 -> Algebra 285 permutation [ 1, 5, 2, 3, 4, 6, 7 ]
vertex 7 -> Algebra 62 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 180
Quiver
[ 1, 4 ], [ 1, 6 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 1 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 4, 3, 5, 1 ]
[ 6, 5, 1 ]
[ 5, 1, 4, 3 ]
[ 3, 5, 1, 4 ]
[ 5, 1, 6 ]
[ 1, 4, 3, 5 ] - [ 1, 6, 5 ]
Cartan matrix
(1 0 1 1 1 1 0)
(1 1 1 0 1 0 0)
(1 0 1 0 1 0 0)
(0 0 1 1 1 0 0)
(1 0 0 1 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 2 -> Algebra 212 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 105 permutation [ 2, 3, 1, 5, 7, 6, 4 ]
vertex 7 -> Algebra 63 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 184
Quiver
[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 3, 4, 5, 1 ]
[ 3, 4, 2 ]
[ 2, 3, 4 ]
[ 5, 1, 3, 4 ]
[ 1, 3, 4, 5 ]
[ 4, 2, 3 ] - [ 4, 5, 1, 3 ]
Cartan matrix
(1 0 1 1 0 0 0)
(0 1 1 0 0 0 0)
(0 0 1 1 1 1 1)
(1 1 1 1 1 1 1)
(1 0 1 0 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 66 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 337 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 187
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 5, 3, 1 ]
[ 3, 4, 2 ]
[ 1, 5, 3 ]
[ 2, 3, 4 ]
[ 5, 3, 4 ]
[ 4, 2, 3 ] - [ 4, 5, 3 ]
[ 3, 1, 5 ] - [ 3, 4, 5 ]
Cartan matrix
(1 0 0 0 1 1 0)
(1 1 1 0 0 0 0)
(1 0 1 1 1 1 0)
(0 1 1 1 1 1 0)
(0 0 1 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 337 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 240 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 177 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 6 -> Algebra 132 permutation [ 1, 5, 2, 4, 3, 6, 7 ]
vertex 7 -> Algebra 66 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 193
Quiver
[ 1, 3 ], [ 2, 3 ], [ 3, 5 ], [ 4, 1 ], [ 5, 2 ], [ 5, 4 ], [ 6, 1 ], [ 6, 7 ]
Relations
[ 3, 5, 4, 1 ]
[ 3, 5, 2 ]
[ 1, 3, 5, 4 ]
[ 2, 3, 5 ]
[ 4, 1, 3, 5 ]
[ 5, 2, 3 ] - [ 5, 4, 1, 3 ]
Cartan matrix
(1 0 1 0 1 0 0)
(0 1 1 0 0 0 0)
(0 0 1 1 1 0 0)
(1 0 1 1 0 0 0)
(1 1 1 1 1 0 0)
(1 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 343 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 295 permutation [ 2, 3, 5, 4, 1, 6, 7 ]
vertex 7 -> Algebra 344 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 209
Quiver
[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 5, 2, 4, 1 ]
[ 4, 1, 5, 2 ]
[ 1, 5, 2, 4 ]
[ 2, 4, 1, 5 ]
Cartan matrix
(1 1 1 0 1 1 0)
(1 1 1 1 0 0 0)
(0 0 1 0 0 0 0)
(1 0 0 1 1 1 0)
(0 1 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 219 permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex 3 -> Algebra 177 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 5 -> Algebra 152 permutation [ 3, 2, 1, 5, 7, 6, 4 ]
vertex 6 -> Algebra 359 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 77 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 212
Quiver
[ 1, 4 ], [ 1, 6 ], [ 2, 3 ], [ 2, 5 ], [ 4, 2 ], [ 5, 1 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 4, 2, 5, 1 ]
[ 6, 5, 1 ]
[ 5, 1, 4, 2 ]
[ 2, 5, 1, 4 ]
[ 5, 1, 6 ]
[ 1, 4, 2, 5 ] - [ 1, 6, 5 ]
Cartan matrix
(1 1 1 1 1 1 0)
(1 1 1 0 1 0 0)
(0 0 1 0 0 0 0)
(0 1 1 1 1 0 0)
(1 0 0 1 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 2 -> Algebra 230 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 3 -> Algebra 180 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 152 permutation [ 3, 2, 1, 5, 7, 6, 4 ]
vertex 7 -> Algebra 78 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 216
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 2, 4, 5, 1 ]
[ 4, 5, 1, 2 ]
[ 4, 5, 3 ]
[ 1, 2, 4, 5 ]
[ 3, 4, 5 ]
[ 5, 1, 2, 4 ] - [ 5, 3, 4 ]
Cartan matrix
(1 1 0 1 0 0 0)
(0 1 0 1 1 1 1)
(0 0 1 1 0 0 0)
(1 0 0 1 1 1 1)
(1 1 1 1 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 81 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 128 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 364 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 366 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 217
Quiver
[ 1, 3 ], [ 1, 6 ], [ 2, 5 ], [ 3, 5 ], [ 4, 6 ], [ 5, 1 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 3, 5, 1 ]
[ 6, 5, 1 ]
[ 5, 1, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 1, 3, 5 ] - [ 1, 6, 5 ]
[ 5, 1, 6 ] - [ 5, 4, 6 ]
Cartan matrix
(1 0 1 0 1 1 1)
(1 1 0 1 1 1 1)
(0 0 1 1 1 0 0)
(0 0 0 1 0 1 1)
(1 0 0 1 1 1 1)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 256 permutation [ 3, 1, 4, 6, 7, 5, 2 ]
vertex 2 -> Algebra 220 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 3 -> Algebra 367 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 318 permutation [ 3, 5, 1, 4, 6, 7, 2 ]
vertex 5 -> Algebra 81 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 369 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 219
Quiver
[ 1, 5 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 5, 2, 1 ]
[ 1, 5, 2 ]
[ 4, 5, 2 ]
[ 4, 5, 3 ]
[ 3, 4, 5 ]
[ 5, 2, 4 ] - [ 5, 3, 4 ]
[ 2, 1, 5 ] - [ 2, 4, 5 ]
Cartan matrix
(1 0 1 0 1 1 0)
(1 1 0 1 1 1 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 1 0)
(0 1 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 366 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 84 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 240 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 4 -> Algebra 209 permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex 5 -> Algebra 369 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 307 permutation [ 1, 5, 2, 3, 4, 6, 7 ]
vertex 7 -> Algebra 81 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 220
Quiver
[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 4 ], [ 2, 5 ], [ 3, 2 ], [ 4, 6 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 6, 2, 1 ]
[ 4, 6, 2 ]
[ 2, 1, 3 ]
[ 6, 2, 4 ]
[ 1, 3, 2 ] - [ 1, 6, 2 ]
[ 2, 1, 6 ] - [ 2, 4, 6 ]
Cartan matrix
(1 1 1 0 1 1 1)
(1 1 0 1 1 1 1)
(0 1 1 1 1 0 0)
(0 0 0 1 0 1 1)
(0 0 0 0 1 0 0)
(0 1 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 102 permutation [ 3, 1, 4, 6, 7, 2, 5 ]
vertex 2 -> Algebra 82 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 372 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 228 permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex 5 -> Algebra 217 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 7 -> Algebra 373 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 221
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 2 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3, 2 ]
[ 2, 6, 5, 3 ]
[ 3, 2, 6, 5 ]
[ 5, 3, 2, 6 ]
Cartan matrix
(1 1 0 0 1 1 1)
(0 1 0 0 1 1 1)
(0 1 1 0 0 1 1)
(0 1 1 1 0 1 1)
(0 1 1 0 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 279 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 373 permutation [ 2, 6, 1, 5, 7, 3, 4 ]
vertex 3 -> Algebra 82 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 102 permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex 6 -> Algebra 374 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 375 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 223
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 2 ]
[ 4, 2, 3 ]
[ 5, 2, 3 ]
[ 2, 3, 4 ]
[ 5, 2, 6 ]
[ 3, 4, 2 ] - [ 3, 5, 2 ]
[ 2, 3, 5 ] - [ 2, 6, 5 ]
Cartan matrix
(1 1 1 0 1 1 0)
(0 1 1 0 1 1 0)
(0 1 1 1 1 0 0)
(0 1 0 1 0 1 0)
(0 1 0 0 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 281 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 373 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 375 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 87 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 84 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 377 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 82 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 225
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 5, 3, 4, 2 ]
[ 4, 2, 5, 3 ]
[ 2, 5, 3, 4 ]
[ 3, 4, 2, 5 ]
Cartan matrix
(1 1 1 0 1 0 0)
(0 1 1 0 1 0 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 0 0)
(0 0 1 1 1 0 0)
(0 0 1 1 1 1 1)
(0 0 1 1 1 0 1)
Good mutations
vertex 1 -> Algebra 283 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 371 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 332 permutation [ 7, 1, 2, 5, 3, 4, 6 ]
vertex 6 -> Algebra 226 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 226
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 5, 3, 4, 2 ]
[ 4, 2, 5, 3 ]
[ 2, 5, 3, 4 ]
[ 3, 4, 2, 5 ]
Cartan matrix
(1 1 1 0 1 0 0)
(0 1 1 0 1 0 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 0 0)
(0 0 1 1 1 0 0)
(0 0 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 284 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 307 permutation [ 1, 5, 2, 3, 4, 6, 7 ]
vertex 5 -> Algebra 265 permutation [ 1, 2, 3, 5, 4, 6, 7 ]
vertex 6 -> Algebra 84 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 225 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 227
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 4, 1 ], [ 4, 3 ], [ 5, 4 ], [ 6, 1 ], [ 6, 7 ]
Relations
[ 2, 5, 4, 1 ]
[ 5, 4, 1, 2 ]
[ 5, 4, 3 ]
[ 1, 2, 5, 4 ]
[ 3, 5, 4 ]
[ 4, 1, 2, 5 ] - [ 4, 3, 5 ]
Cartan matrix
(1 1 0 0 1 0 0)
(0 1 0 1 1 0 0)
(0 0 1 0 1 0 0)
(1 1 1 1 1 0 0)
(1 0 0 1 1 0 0)
(1 1 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 85 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 132 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 337 permutation [ 2, 3, 5, 4, 1, 6, 7 ]
vertex 7 -> Algebra 379 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 228
Quiver
[ 1, 3 ], [ 1, 6 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 3, 4, 1 ]
[ 6, 2, 4, 1 ]
[ 4, 1, 6, 2 ]
[ 4, 1, 3 ]
[ 2, 4, 1, 6 ]
[ 1, 3, 4 ] - [ 1, 6, 2, 4 ]
Cartan matrix
(1 1 1 1 1 1 1)
(1 1 0 1 1 0 0)
(0 0 1 1 1 0 0)
(1 0 0 1 1 1 1)
(0 0 0 0 1 0 0)
(0 1 0 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 220 permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex 4 -> Algebra 85 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 318 permutation [ 3, 4, 1, 2, 6, 7, 5 ]
vertex 7 -> Algebra 241 permutation [ 3, 1, 7, 2, 6, 4, 5 ]
Algebra 230
Quiver
[ 1, 4 ], [ 1, 6 ], [ 2, 1 ], [ 2, 5 ], [ 3, 5 ], [ 4, 2 ], [ 4, 3 ], [ 5, 4 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 4, 2, 1 ]
[ 6, 2, 1 ]
[ 5, 4, 2 ]
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 2, 1, 6 ]
[ 1, 4, 2 ] - [ 1, 6, 2 ]
[ 2, 1, 4 ] - [ 2, 5, 4 ]
[ 4, 2, 5 ] - [ 4, 3, 5 ]
Cartan matrix
(1 1 1 1 1 1 0)
(1 1 0 1 1 0 0)
(0 0 1 0 1 0 0)
(0 1 1 1 1 0 0)
(0 0 0 1 1 0 0)
(0 1 0 0 1 1 0)
(0 1 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 379 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 87 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 241 permutation [ 3, 1, 7, 2, 6, 4, 5 ]
vertex 5 -> Algebra 212 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 7 -> Algebra 85 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 235
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 7 ], [ 6, 7 ], [ 7, 3 ]
Relations
[ 4, 3, 5, 2 ]
[ 3, 5, 2, 4 ]
[ 2, 4, 3, 5 ]
[ 7, 3, 5 ]
[ 3, 5, 7 ]
[ 5, 2, 4, 3 ] - [ 5, 7, 3 ]
Cartan matrix
(1 1 1 1 0 0 0)
(0 1 1 1 0 0 0)
(0 1 1 0 1 0 0)
(0 0 1 1 1 0 0)
(0 1 1 1 1 0 1)
(0 0 1 0 0 1 1)
(0 0 1 0 0 0 1)
Good mutations
vertex 1 -> Algebra 291 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 348 permutation [ 7, 1, 4, 5, 2, 3, 6 ]
vertex 4 -> Algebra 332 permutation [ 7, 1, 2, 5, 3, 4, 6 ]
vertex 6 -> Algebra 236 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 236
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 6 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 4, 3, 5, 2 ]
[ 3, 5, 2, 4 ]
[ 2, 4, 3, 5 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 2, 4, 3 ] - [ 5, 6, 3 ]
Cartan matrix
(1 1 1 1 0 0 0)
(0 1 1 1 0 0 0)
(0 1 1 0 1 0 0)
(0 0 1 1 1 0 0)
(0 1 1 1 1 1 1)
(0 0 1 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 292 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 293 permutation [ 1, 4, 2, 5, 3, 6, 7 ]
vertex 4 -> Algebra 265 permutation [ 1, 2, 3, 5, 4, 6, 7 ]
vertex 7 -> Algebra 235 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 238
Quiver
[ 1, 6 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 4, 6 ], [ 5, 1 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 1 ]
[ 3, 4, 2 ]
[ 5, 4, 2 ]
[ 4, 2, 3 ]
[ 6, 5, 4 ]
[ 1, 6, 5 ]
[ 2, 3, 4 ] - [ 2, 5, 4 ]
[ 4, 2, 5 ] - [ 4, 6, 5 ]
[ 5, 1, 6 ] - [ 5, 4, 6 ]
Cartan matrix
(1 0 0 0 0 1 1)
(1 1 1 1 1 1 1)
(0 0 1 1 0 1 1)
(0 1 0 1 1 1 1)
(1 0 0 1 1 1 1)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 241 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 4 -> Algebra 367 permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex 5 -> Algebra 91 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 312 permutation [ 1, 6, 2, 4, 3, 5, 7 ]
Algebra 240
Quiver
[ 1, 5 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 5, 2, 1 ]
[ 1, 5, 2 ]
[ 3, 4, 5, 2 ]
[ 4, 5, 2, 3 ]
[ 5, 2, 3, 4 ]
[ 2, 1, 5 ] - [ 2, 3, 4, 5 ]
Cartan matrix
(1 0 0 0 1 1 0)
(1 1 1 1 1 1 0)
(0 0 1 1 1 1 0)
(0 1 0 1 1 1 0)
(0 1 1 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 3 -> Algebra 187 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 219 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 312 permutation [ 1, 6, 2, 4, 3, 5, 7 ]
vertex 6 -> Algebra 148 permutation [ 1, 5, 2, 4, 3, 6, 7 ]
vertex 7 -> Algebra 91 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 241
Quiver
[ 1, 6 ], [ 2, 1 ], [ 2, 5 ], [ 3, 5 ], [ 4, 6 ], [ 5, 4 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 6, 2, 1 ]
[ 1, 6, 2 ]
[ 5, 4, 6, 2 ]
[ 6, 2, 5, 4 ]
[ 4, 6, 2, 5 ]
[ 2, 1, 6 ] - [ 2, 5, 4, 6 ]
Cartan matrix
(1 0 0 0 0 1 1)
(1 1 0 1 1 1 1)
(0 0 1 1 1 1 1)
(0 1 0 1 0 1 1)
(0 0 0 1 1 1 1)
(0 1 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 228 permutation [ 2, 4, 1, 6, 7, 5, 3 ]
vertex 4 -> Algebra 373 permutation [ 2, 6, 1, 4, 7, 5, 3 ]
vertex 5 -> Algebra 238 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 6 -> Algebra 230 permutation [ 2, 4, 1, 6, 7, 5, 3 ]
vertex 7 -> Algebra 315 permutation [ 1, 6, 2, 4, 3, 5, 7 ]
Algebra 255
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 4, 5 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 7, 6, 2 ]
[ 4, 2, 3 ]
[ 6, 2, 3 ]
[ 2, 3, 4 ]
[ 6, 2, 7 ]
[ 3, 4, 2 ] - [ 3, 6, 2 ]
[ 2, 3, 6 ] - [ 2, 7, 6 ]
Cartan matrix
(1 1 1 0 0 1 1)
(0 1 1 0 0 1 1)
(0 1 1 1 1 1 0)
(0 1 0 1 1 0 1)
(0 0 0 0 1 0 0)
(0 1 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 310 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 129 permutation [ 6, 2, 1, 3, 7, 4, 5 ]
vertex 3 -> Algebra 285 permutation [ 6, 3, 1, 2, 7, 4, 5 ]
vertex 4 -> Algebra 103 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 374 permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex 6 -> Algebra 102 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 276 permutation [ 6, 7, 1, 3, 2, 4, 5 ]
Algebra 256
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 6, 3, 4, 2 ]
[ 4, 2, 6, 3 ]
[ 2, 6, 3, 4 ]
[ 3, 4, 2, 6 ]
Cartan matrix
(1 1 1 0 0 1 0)
(0 1 1 0 0 1 0)
(0 1 1 1 1 0 0)
(0 1 0 1 1 1 0)
(0 0 0 0 1 0 0)
(0 0 1 1 1 1 0)
(0 0 1 1 1 1 1)
Good mutations
vertex 1 -> Algebra 311 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 217 permutation [ 2, 7, 1, 3, 6, 4, 5 ]
vertex 4 -> Algebra 104 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 375 permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex 6 -> Algebra 364 permutation [ 6, 7, 1, 3, 2, 4, 5 ]
vertex 7 -> Algebra 102 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 265
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 6 ], [ 5, 2 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 5, 2, 3 ]
[ 2, 3, 4 ]
[ 6, 3, 4 ]
[ 2, 3, 5 ]
[ 3, 4, 6 ]
[ 3, 4, 2 ] - [ 3, 5, 2 ]
[ 4, 2, 3 ] - [ 4, 6, 3 ]
Cartan matrix
(1 1 1 0 0 0 0)
(0 1 1 0 0 0 0)
(0 1 1 1 1 0 0)
(0 1 1 1 0 1 1)
(0 1 0 0 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 320 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 301 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 226 permutation [ 1, 2, 3, 5, 4, 6, 7 ]
vertex 5 -> Algebra 236 permutation [ 1, 2, 3, 5, 4, 6, 7 ]
vertex 6 -> Algebra 377 permutation [ 1, 2, 3, 5, 6, 4, 7 ]
vertex 7 -> Algebra 332 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
Algebra 276
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 4, 1 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 2, 5, 4, 1 ]
[ 5, 4, 1, 2 ]
[ 1, 2, 5, 4 ]
[ 6, 5, 4 ]
[ 5, 4, 6 ]
[ 4, 1, 2, 5 ] - [ 4, 6, 5 ]
Cartan matrix
(1 1 0 0 1 0 0)
(0 1 0 1 1 0 0)
(1 0 1 1 1 0 0)
(1 1 0 1 1 1 1)
(1 0 0 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 364 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 255 permutation [ 3, 5, 4, 6, 7, 1, 2 ]
vertex 3 -> Algebra 363 permutation [ 1, 5, 3, 2, 4, 6, 7 ]
vertex 5 -> Algebra 128 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 334 permutation [ 1, 3, 5, 2, 4, 7, 6 ]
Algebra 278
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 2, 4, 1 ]
[ 4, 5, 3 ]
[ 1, 2, 4 ]
[ 2, 4, 5 ]
[ 3, 4, 5 ]
[ 4, 1, 2 ] - [ 4, 5, 2 ]
[ 5, 2, 4 ] - [ 5, 3, 4 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 1 0 0 0)
(1 0 1 1 0 0 0)
(1 1 0 1 1 1 0)
(0 1 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 366 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 131 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 295 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 334 permutation [ 1, 3, 5, 2, 4, 7, 6 ]
vertex 6 -> Algebra 343 permutation [ 5, 1, 2, 3, 4, 6, 7 ]
vertex 7 -> Algebra 128 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 279
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 2 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3, 2 ]
[ 2, 6, 5, 3 ]
[ 3, 2, 6, 5 ]
[ 5, 3, 2, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 1 1 1)
(1 1 1 0 0 1 1)
(1 1 1 1 0 1 1)
(1 1 1 0 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 221 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 403 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 129 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 149 permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex 6 -> Algebra 404 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 405 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 281
Quiver
[ 2, 1 ], [ 2, 3 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 2 ]
[ 4, 2, 3 ]
[ 5, 2, 3 ]
[ 2, 3, 4 ]
[ 5, 2, 6 ]
[ 3, 4, 2 ] - [ 3, 5, 2 ]
[ 2, 3, 5 ] - [ 2, 6, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 1 0)
(1 1 1 1 1 0 0)
(1 1 0 1 0 1 0)
(1 1 0 0 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 223 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 374 permutation [ 3, 2, 6, 7, 4, 1, 5 ]
vertex 3 -> Algebra 405 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 134 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 131 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 406 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 129 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 283
Quiver
[ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 5, 3, 4, 2 ]
[ 4, 2, 5, 3 ]
[ 2, 5, 3, 4 ]
[ 3, 4, 2, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 0 0)
(1 1 1 1 0 0 0)
(1 1 0 1 1 0 0)
(0 0 1 1 1 0 0)
(0 0 1 1 1 1 1)
(0 0 1 1 1 0 1)
Good mutations
vertex 1 -> Algebra 225 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 354 permutation [ 1, 3, 4, 2, 6, 7, 5 ]
vertex 5 -> Algebra 360 permutation [ 7, 2, 1, 5, 3, 4, 6 ]
vertex 6 -> Algebra 284 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 284
Quiver
[ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 5, 3, 4, 2 ]
[ 4, 2, 5, 3 ]
[ 2, 5, 3, 4 ]
[ 3, 4, 2, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 0 0)
(1 1 1 1 0 0 0)
(1 1 0 1 1 0 0)
(0 0 1 1 1 0 0)
(0 0 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 226 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 343 permutation [ 5, 1, 2, 3, 4, 6, 7 ]
vertex 5 -> Algebra 320 permutation [ 2, 1, 3, 5, 4, 6, 7 ]
vertex 6 -> Algebra 131 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 283 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 285
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 2, 4, 5, 1 ]
[ 4, 5, 1, 2 ]
[ 5, 1, 2, 4 ]
[ 1, 2, 4, 5 ]
Cartan matrix
(1 1 0 1 0 0 0)
(0 1 0 1 1 0 0)
(1 0 1 1 1 0 0)
(1 0 0 1 1 0 0)
(1 1 0 0 1 0 0)
(0 1 0 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 255 permutation [ 3, 4, 2, 6, 7, 1, 5 ]
vertex 3 -> Algebra 359 permutation [ 1, 4, 3, 5, 2, 6, 7 ]
vertex 4 -> Algebra 132 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 177 permutation [ 1, 3, 4, 5, 2, 6, 7 ]
vertex 7 -> Algebra 331 permutation [ 1, 3, 4, 5, 2, 7, 6 ]
Algebra 286
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 4, 2 ], [ 4, 3 ], [ 5, 1 ], [ 5, 4 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 2, 5, 1 ]
[ 5, 4, 3 ]
[ 2, 5, 4 ]
[ 3, 5, 4 ]
[ 1, 2, 5 ]
[ 5, 1, 2 ] - [ 5, 4, 2 ]
[ 4, 2, 5 ] - [ 4, 3, 5 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 1 0 0)
(1 0 1 0 1 0 0)
(0 1 1 1 1 0 0)
(1 1 0 1 1 0 0)
(0 1 0 0 1 1 0)
(0 1 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 379 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 134 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 308 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 331 permutation [ 1, 3, 4, 5, 2, 7, 6 ]
vertex 7 -> Algebra 132 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 291
Quiver
[ 2, 1 ], [ 2, 4 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 7 ], [ 6, 7 ], [ 7, 3 ]
Relations
[ 4, 3, 5, 2 ]
[ 3, 5, 2, 4 ]
[ 2, 4, 3, 5 ]
[ 7, 3, 5 ]
[ 3, 5, 7 ]
[ 5, 2, 4, 3 ] - [ 5, 7, 3 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 0 0)
(1 1 1 0 1 0 0)
(0 0 1 1 1 0 0)
(1 1 1 1 1 0 1)
(0 0 1 0 0 1 1)
(0 0 1 0 0 0 1)
Good mutations
vertex 1 -> Algebra 235 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 360 permutation [ 7, 2, 1, 5, 3, 4, 6 ]
vertex 6 -> Algebra 292 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 292
Quiver
[ 2, 1 ], [ 2, 4 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 6 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 4, 3, 5, 2 ]
[ 3, 5, 2, 4 ]
[ 2, 4, 3, 5 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 2, 4, 3 ] - [ 5, 6, 3 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 0 0)
(1 1 1 0 1 0 0)
(0 0 1 1 1 0 0)
(1 1 1 1 1 1 1)
(0 0 1 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 236 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 320 permutation [ 2, 1, 3, 5, 4, 6, 7 ]
vertex 7 -> Algebra 291 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 293
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 2, 3, 1 ]
[ 5, 4, 2 ]
[ 1, 2, 3 ]
[ 4, 2, 3 ]
[ 6, 5, 4 ]
[ 5, 4, 6 ]
[ 3, 1, 2 ] - [ 3, 4, 2 ]
[ 2, 3, 4 ] - [ 2, 5, 4 ]
[ 4, 2, 5 ] - [ 4, 6, 5 ]
Cartan matrix
(1 1 0 0 1 0 0)
(0 1 1 1 1 0 0)
(1 1 1 1 1 1 1)
(0 1 0 1 1 1 1)
(0 0 0 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 296 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 3 -> Algebra 236 permutation [ 1, 3, 5, 2, 4, 6, 7 ]
vertex 4 -> Algebra 363 permutation [ 1, 4, 5, 2, 3, 6, 7 ]
vertex 5 -> Algebra 138 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 348 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
Algebra 295
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 2, 3, 1 ]
[ 1, 2, 3 ]
[ 4, 5, 2, 3 ]
[ 5, 2, 3, 4 ]
[ 2, 3, 4, 5 ]
[ 3, 1, 2 ] - [ 3, 4, 5, 2 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 1 1 0 0 0)
(1 1 1 1 1 1 0)
(0 1 0 1 1 1 0)
(0 1 1 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 4 -> Algebra 278 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 348 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
vertex 6 -> Algebra 193 permutation [ 5, 1, 2, 4, 3, 6, 7 ]
vertex 7 -> Algebra 138 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 296
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 4, 6 ], [ 5, 1 ], [ 5, 4 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 2, 5, 1 ]
[ 6, 2, 5, 4 ]
[ 1, 2, 5 ]
[ 4, 6, 2, 5 ]
[ 2, 5, 4, 6 ]
[ 5, 1, 2 ] - [ 5, 4, 6, 2 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 1 1 0 0)
(1 1 1 1 1 1 1)
(0 1 0 1 0 1 1)
(1 1 0 1 1 1 1)
(0 1 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 301 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 403 permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex 5 -> Algebra 293 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 6 -> Algebra 407 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 351 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
Algebra 301
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 5 ], [ 4, 6 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 2, 3, 1 ]
[ 1, 2, 3 ]
[ 4, 6, 2, 3 ]
[ 6, 2, 3, 4 ]
[ 2, 3, 4, 6 ]
[ 3, 1, 2 ] - [ 3, 4, 6, 2 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 1 1 1 0 0)
(1 1 1 1 1 1 1)
(0 1 0 1 0 1 1)
(0 0 0 0 1 0 0)
(0 1 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 265 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 309 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 296 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 393 permutation [ 1, 4, 7, 2, 6, 3, 5 ]
vertex 7 -> Algebra 355 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
Algebra 307
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 4 ], [ 3, 1 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 2, 3, 1 ]
[ 4, 5, 2 ]
[ 1, 2, 3 ]
[ 5, 2, 3 ]
[ 5, 2, 4 ]
[ 3, 1, 2 ] - [ 3, 5, 2 ]
[ 2, 3, 5 ] - [ 2, 4, 5 ]
Cartan matrix
(1 1 0 1 0 0 0)
(0 1 1 1 1 0 0)
(1 1 1 0 1 0 0)
(0 0 0 1 1 0 0)
(0 1 0 0 1 0 0)
(0 1 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 391 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 309 permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex 3 -> Algebra 226 permutation [ 1, 3, 4, 5, 2, 6, 7 ]
vertex 4 -> Algebra 148 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 359 permutation [ 1, 5, 4, 3, 2, 6, 7 ]
vertex 6 -> Algebra 219 permutation [ 1, 3, 4, 5, 2, 6, 7 ]
vertex 7 -> Algebra 371 permutation [ 1, 3, 4, 5, 2, 7, 6 ]
Algebra 308
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 2 ], [ 5, 4 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 2, 3, 1 ]
[ 1, 2, 3 ]
[ 5, 4, 2, 3 ]
[ 2, 3, 5, 4 ]
[ 4, 2, 3, 5 ]
[ 3, 1, 2 ] - [ 3, 5, 4, 2 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 1 0 1 0 0)
(1 1 1 1 1 0 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 0 0)
(0 1 1 0 1 1 0)
(0 1 1 0 1 1 1)
Good mutations
vertex 2 -> Algebra 151 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 371 permutation [ 1, 3, 4, 5, 2, 7, 6 ]
vertex 5 -> Algebra 286 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 7 -> Algebra 148 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 309
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 4, 6 ], [ 6, 2 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 2, 4, 1 ]
[ 4, 6, 3 ]
[ 1, 2, 4 ]
[ 2, 4, 6 ]
[ 3, 4, 6 ]
[ 4, 1, 2 ] - [ 4, 6, 2 ]
[ 6, 2, 4 ] - [ 6, 3, 4 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 1 1 0 0)
(1 0 1 1 1 0 0)
(1 1 0 1 1 1 1)
(0 0 0 0 1 0 0)
(0 1 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 372 permutation [ 1, 6, 2, 3, 7, 4, 5 ]
vertex 2 -> Algebra 149 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 301 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 4 -> Algebra 307 permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex 5 -> Algebra 403 permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex 6 -> Algebra 409 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 410 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 310
Quiver
[ 2, 1 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 4, 5 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 7, 6, 2 ]
[ 4, 2, 3 ]
[ 6, 2, 3 ]
[ 2, 3, 4 ]
[ 6, 2, 7 ]
[ 3, 4, 2 ] - [ 3, 6, 2 ]
[ 2, 3, 6 ] - [ 2, 7, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 0 1 1)
(1 1 1 1 1 1 0)
(1 1 0 1 1 0 1)
(0 0 0 0 1 0 0)
(1 1 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 255 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 403 permutation [ 6, 1, 2, 3, 7, 4, 5 ]
vertex 3 -> Algebra 359 permutation [ 6, 2, 1, 7, 3, 4, 5 ]
vertex 4 -> Algebra 150 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 404 permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex 6 -> Algebra 149 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 363 permutation [ 6, 2, 1, 7, 3, 4, 5 ]
Algebra 311
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 6, 3, 4, 2 ]
[ 4, 2, 6, 3 ]
[ 2, 6, 3, 4 ]
[ 3, 4, 2, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 0 1 0)
(1 1 1 1 1 0 0)
(1 1 0 1 1 1 0)
(0 0 0 0 1 0 0)
(0 0 1 1 1 1 0)
(0 0 1 1 1 1 1)
Good mutations
vertex 1 -> Algebra 256 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 410 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 151 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 405 permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex 6 -> Algebra 411 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 149 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 312
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 5 ], [ 3, 6 ], [ 4, 2 ], [ 4, 3 ], [ 5, 4 ], [ 6, 1 ], [ 6, 4 ], [ 7, 2 ]
Relations
[ 2, 6, 1 ]
[ 5, 4, 3 ]
[ 6, 4, 3 ]
[ 2, 6, 4 ]
[ 4, 3, 5 ]
[ 1, 2, 6 ]
[ 6, 1, 2 ] - [ 6, 4, 2 ]
[ 3, 5, 4 ] - [ 3, 6, 4 ]
[ 4, 2, 6 ] - [ 4, 3, 6 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 1 0)
(1 1 1 1 1 1 0)
(0 1 1 1 0 1 0)
(0 1 0 1 1 0 0)
(1 1 0 1 0 1 0)
(0 1 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 150 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 315 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 4 -> Algebra 412 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 240 permutation [ 1, 3, 5, 4, 6, 2, 7 ]
vertex 7 -> Algebra 238 permutation [ 1, 3, 5, 4, 6, 2, 7 ]
Algebra 315
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 6 ], [ 4, 2 ], [ 5, 6 ], [ 6, 4 ], [ 7, 2 ]
Relations
[ 2, 3, 1 ]
[ 1, 2, 3 ]
[ 6, 4, 2, 3 ]
[ 2, 3, 6, 4 ]
[ 4, 2, 3, 6 ]
[ 3, 1, 2 ] - [ 3, 6, 4, 2 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 1 0 0 1 0)
(1 1 1 1 0 1 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 1 0)
(0 1 0 1 0 1 0)
(0 1 1 0 0 1 1)
Good mutations
vertex 2 -> Algebra 152 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 369 permutation [ 3, 7, 1, 4, 2, 6, 5 ]
vertex 5 -> Algebra 318 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 312 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 7 -> Algebra 241 permutation [ 1, 3, 5, 4, 6, 2, 7 ]
Algebra 318
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 7, 2 ]
Relations
[ 2, 3, 1 ]
[ 1, 2, 3 ]
[ 5, 4, 2, 3 ]
[ 2, 3, 5, 4 ]
[ 4, 2, 3, 5 ]
[ 3, 1, 2 ] - [ 3, 5, 4, 2 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 1 0 1 1 0)
(1 1 1 1 1 1 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 1 0)
(0 0 0 0 0 1 0)
(0 1 1 0 1 1 1)
Good mutations
vertex 2 -> Algebra 155 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 217 permutation [ 3, 7, 1, 4, 2, 5, 6 ]
vertex 6 -> Algebra 315 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 228 permutation [ 3, 4, 1, 2, 7, 5, 6 ]
Algebra 320
Quiver
[ 1, 2 ], [ 1, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 1 ], [ 4, 6 ], [ 5, 1 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 5, 1, 3 ]
[ 1, 3, 4 ]
[ 6, 3, 4 ]
[ 1, 3, 5 ]
[ 3, 4, 6 ]
[ 3, 4, 1 ] - [ 3, 5, 1 ]
[ 4, 1, 3 ] - [ 4, 6, 3 ]
Cartan matrix
(1 1 1 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 1 1 0 0)
(1 1 1 1 0 1 1)
(1 1 0 0 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 265 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 284 permutation [ 2, 1, 3, 5, 4, 6, 7 ]
vertex 5 -> Algebra 292 permutation [ 2, 1, 3, 5, 4, 6, 7 ]
vertex 6 -> Algebra 406 permutation [ 2, 1, 3, 5, 6, 4, 7 ]
vertex 7 -> Algebra 360 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
Algebra 331
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 5, 3, 4, 1 ]
[ 4, 1, 5, 3 ]
[ 1, 5, 3, 4 ]
[ 3, 4, 1, 5 ]
Cartan matrix
(1 0 1 0 1 0 0)
(1 1 1 1 0 0 0)
(1 0 1 1 0 0 0)
(1 0 0 1 1 0 0)
(0 0 1 1 1 0 0)
(0 0 1 1 1 1 1)
(0 0 1 1 1 0 1)
Good mutations
vertex 2 -> Algebra 358 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 286 permutation [ 1, 5, 2, 3, 4, 7, 6 ]
vertex 5 -> Algebra 374 permutation [ 2, 3, 7, 6, 5, 1, 4 ]
vertex 6 -> Algebra 285 permutation [ 1, 5, 2, 3, 4, 7, 6 ]
Algebra 332
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 5 ], [ 4, 1 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ]
Relations
[ 5, 4, 1 ]
[ 1, 5, 4 ]
[ 3, 5, 4 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 4, 3 ] - [ 5, 6, 3 ]
[ 4, 1, 5 ] - [ 4, 3, 5 ]
Cartan matrix
(1 0 0 0 1 1 0)
(0 1 1 0 1 0 0)
(0 0 1 0 1 0 0)
(1 0 1 1 1 0 0)
(0 0 1 1 1 1 0)
(0 0 1 0 0 1 0)
(1 0 0 0 1 1 1)
Good mutations
vertex 2 -> Algebra 360 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 355 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 225 permutation [ 2, 3, 5, 6, 4, 7, 1 ]
vertex 6 -> Algebra 235 permutation [ 2, 3, 5, 6, 4, 7, 1 ]
vertex 7 -> Algebra 265 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
Algebra 334
Quiver
[ 1, 4 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 1 ], [ 5, 7 ], [ 6, 7 ], [ 7, 3 ]
Relations
[ 4, 3, 5, 1 ]
[ 3, 5, 1, 4 ]
[ 1, 4, 3, 5 ]
[ 7, 3, 5 ]
[ 3, 5, 7 ]
[ 5, 1, 4, 3 ] - [ 5, 7, 3 ]
Cartan matrix
(1 0 1 1 0 0 0)
(1 1 1 0 1 0 0)
(1 0 1 0 1 0 0)
(0 0 1 1 1 0 0)
(1 0 1 1 1 0 1)
(0 0 1 0 0 1 1)
(0 0 1 0 0 0 1)
Good mutations
vertex 1 -> Algebra 402 permutation [ 2, 3, 5, 4, 6, 7, 1 ]
vertex 2 -> Algebra 362 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 278 permutation [ 1, 4, 2, 5, 3, 7, 6 ]
vertex 4 -> Algebra 374 permutation [ 2, 3, 7, 6, 5, 1, 4 ]
vertex 6 -> Algebra 276 permutation [ 1, 4, 2, 5, 3, 7, 6 ]
Algebra 337
Quiver
[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 3, 4, 5, 1 ]
[ 3, 4, 2 ]
[ 2, 3, 4 ]
[ 5, 1, 3, 4 ]
[ 1, 3, 4, 5 ]
[ 4, 2, 3 ] - [ 4, 5, 1, 3 ]
Cartan matrix
(1 0 1 1 0 0 0)
(0 1 1 0 0 0 0)
(0 0 1 1 1 1 0)
(1 1 1 1 1 1 0)
(1 0 1 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 187 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 227 permutation [ 5, 1, 2, 4, 3, 6, 7 ]
vertex 7 -> Algebra 184 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 343
Quiver
[ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 1 ], [ 5, 2 ], [ 6, 1 ], [ 6, 7 ]
Relations
[ 3, 5, 1 ]
[ 4, 5, 1 ]
[ 3, 5, 2 ]
[ 5, 1, 4 ]
[ 2, 3, 5 ]
[ 5, 1, 3 ] - [ 5, 2, 3 ]
[ 1, 3, 5 ] - [ 1, 4, 5 ]
Cartan matrix
(1 0 1 1 1 0 0)
(0 1 1 0 0 0 0)
(0 0 1 0 1 0 0)
(0 1 0 1 1 0 0)
(1 1 1 0 1 0 0)
(1 0 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 391 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 284 permutation [ 2, 3, 4, 5, 1, 6, 7 ]
vertex 4 -> Algebra 193 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 278 permutation [ 2, 3, 4, 5, 1, 6, 7 ]
vertex 7 -> Algebra 354 permutation [ 2, 4, 5, 3, 7, 6, 1 ]
Algebra 344
Quiver
[ 1, 3 ], [ 2, 3 ], [ 3, 5 ], [ 4, 1 ], [ 5, 2 ], [ 5, 4 ], [ 6, 1 ], [ 7, 6 ]
Relations
[ 3, 5, 4, 1 ]
[ 3, 5, 2 ]
[ 1, 3, 5, 4 ]
[ 2, 3, 5 ]
[ 4, 1, 3, 5 ]
[ 5, 2, 3 ] - [ 5, 4, 1, 3 ]
Cartan matrix
(1 0 1 0 1 0 0)
(0 1 1 0 0 0 0)
(0 0 1 1 1 0 0)
(1 0 1 1 0 0 0)
(1 1 1 1 1 0 0)
(1 0 1 0 1 1 0)
(1 0 1 0 1 1 1)
Good mutations
vertex 4 -> Algebra 354 permutation [ 2, 4, 5, 3, 7, 6, 1 ]
vertex 7 -> Algebra 193 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 348
Quiver
[ 1, 6 ], [ 2, 3 ], [ 3, 5 ], [ 3, 6 ], [ 4, 1 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 6, 4 ], [ 7, 1 ]
Relations
[ 6, 4, 1 ]
[ 3, 5, 2 ]
[ 6, 4, 3 ]
[ 1, 6, 4 ]
[ 2, 3, 5 ]
[ 4, 3, 5 ]
[ 5, 2, 3 ] - [ 5, 4, 3 ]
[ 3, 5, 4 ] - [ 3, 6, 4 ]
[ 4, 1, 6 ] - [ 4, 3, 6 ]
Cartan matrix
(1 0 0 0 0 1 0)
(0 1 1 0 0 1 0)
(0 0 1 1 1 1 0)
(1 0 1 1 0 1 0)
(1 1 1 1 1 1 0)
(0 0 0 1 0 1 0)
(1 0 0 0 0 1 1)
Good mutations
vertex 3 -> Algebra 351 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 4 -> Algebra 362 permutation [ 2, 4, 6, 3, 5, 7, 1 ]
vertex 5 -> Algebra 235 permutation [ 2, 5, 6, 3, 4, 7, 1 ]
vertex 6 -> Algebra 295 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
vertex 7 -> Algebra 293 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
Algebra 351
Quiver
[ 1, 3 ], [ 2, 3 ], [ 3, 6 ], [ 4, 1 ], [ 5, 6 ], [ 6, 2 ], [ 6, 4 ], [ 7, 1 ]
Relations
[ 3, 6, 4, 1 ]
[ 3, 6, 2 ]
[ 1, 3, 6, 4 ]
[ 2, 3, 6 ]
[ 4, 1, 3, 6 ]
[ 6, 2, 3 ] - [ 6, 4, 1, 3 ]
Cartan matrix
(1 0 1 0 0 1 0)
(0 1 1 0 0 0 0)
(0 0 1 1 0 1 0)
(1 0 1 1 0 0 0)
(1 1 1 1 1 1 0)
(1 1 1 1 0 1 0)
(1 0 1 0 0 1 1)
Good mutations
vertex 4 -> Algebra 415 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 355 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 348 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 7 -> Algebra 296 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
Algebra 354
Quiver
[ 1, 4 ], [ 2, 3 ], [ 3, 1 ], [ 3, 7 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 2 ], [ 7, 4 ]
Relations
[ 4, 3, 1 ]
[ 3, 7, 2 ]
[ 1, 4, 3 ]
[ 2, 3, 7 ]
[ 4, 3, 7 ]
[ 7, 2, 3 ] - [ 7, 4, 3 ]
[ 3, 1, 4 ] - [ 3, 7, 4 ]
Cartan matrix
(1 0 0 1 0 0 0)
(1 1 1 0 0 0 0)
(1 0 1 1 0 0 1)
(0 0 1 1 0 0 0)
(0 1 1 1 1 1 1)
(0 1 1 1 0 1 1)
(0 1 1 1 0 0 1)
Good mutations
vertex 1 -> Algebra 408 permutation [ 2, 3, 5, 4, 6, 7, 1 ]
vertex 2 -> Algebra 344 permutation [ 7, 1, 4, 2, 3, 6, 5 ]
vertex 4 -> Algebra 283 permutation [ 1, 4, 2, 3, 7, 5, 6 ]
vertex 5 -> Algebra 343 permutation [ 7, 1, 4, 2, 3, 6, 5 ]
Algebra 355
Quiver
[ 1, 3 ], [ 2, 3 ], [ 3, 5 ], [ 4, 1 ], [ 5, 2 ], [ 5, 4 ], [ 5, 6 ], [ 7, 1 ]
Relations
[ 3, 5, 4, 1 ]
[ 3, 5, 2 ]
[ 1, 3, 5, 4 ]
[ 2, 3, 5 ]
[ 4, 1, 3, 5 ]
[ 5, 2, 3 ] - [ 5, 4, 1, 3 ]
Cartan matrix
(1 0 1 0 1 1 0)
(0 1 1 0 0 0 0)
(0 0 1 1 1 1 0)
(1 0 1 1 0 0 0)
(1 1 1 1 1 1 0)
(0 0 0 0 0 1 0)
(1 0 1 0 1 1 1)
Good mutations
vertex 4 -> Algebra 410 permutation [ 2, 3, 4, 5, 6, 1, 7 ]
vertex 5 -> Algebra 332 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 351 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 301 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
Algebra 358
Quiver
[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 5, 2 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 5, 2, 4, 1 ]
[ 4, 1, 5, 2 ]
[ 1, 5, 2, 4 ]
[ 2, 4, 1, 5 ]
Cartan matrix
(1 1 1 0 1 0 0)
(1 1 1 1 0 0 0)
(0 0 1 0 0 0 0)
(1 0 0 1 1 0 0)
(0 1 1 1 1 0 0)
(0 1 1 1 1 1 1)
(0 1 1 1 1 0 1)
Good mutations
vertex 2 -> Algebra 371 permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex 3 -> Algebra 331 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 5 -> Algebra 404 permutation [ 3, 2, 7, 6, 5, 1, 4 ]
vertex 6 -> Algebra 359 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 359
Quiver
[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 5, 2, 4, 1 ]
[ 4, 1, 5, 2 ]
[ 1, 5, 2, 4 ]
[ 2, 4, 1, 5 ]
Cartan matrix
(1 1 1 0 1 0 0)
(1 1 1 1 0 0 0)
(0 0 1 0 0 0 0)
(1 0 0 1 1 0 0)
(0 1 1 1 1 0 0)
(0 1 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 307 permutation [ 1, 5, 4, 3, 2, 6, 7 ]
vertex 3 -> Algebra 285 permutation [ 1, 5, 3, 2, 4, 6, 7 ]
vertex 5 -> Algebra 310 permutation [ 3, 2, 5, 6, 7, 1, 4 ]
vertex 6 -> Algebra 209 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 358 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 360
Quiver
[ 1, 5 ], [ 2, 3 ], [ 2, 5 ], [ 4, 1 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 2 ], [ 7, 1 ]
Relations
[ 5, 4, 1 ]
[ 1, 5, 4 ]
[ 2, 5, 4 ]
[ 6, 2, 5 ]
[ 2, 5, 6 ]
[ 5, 4, 2 ] - [ 5, 6, 2 ]
[ 4, 1, 5 ] - [ 4, 2, 5 ]
Cartan matrix
(1 0 0 0 1 1 0)
(0 1 1 0 1 0 0)
(0 0 1 0 0 0 0)
(1 1 1 1 1 0 0)
(0 1 1 1 1 1 0)
(0 1 1 0 0 1 0)
(1 0 0 0 1 1 1)
Good mutations
vertex 3 -> Algebra 332 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 283 permutation [ 3, 2, 5, 6, 4, 7, 1 ]
vertex 6 -> Algebra 291 permutation [ 3, 2, 5, 6, 4, 7, 1 ]
vertex 7 -> Algebra 320 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
Algebra 362
Quiver
[ 1, 4 ], [ 2, 3 ], [ 2, 5 ], [ 4, 2 ], [ 5, 1 ], [ 5, 7 ], [ 6, 7 ], [ 7, 2 ]
Relations
[ 4, 2, 5, 1 ]
[ 2, 5, 1, 4 ]
[ 1, 4, 2, 5 ]
[ 7, 2, 5 ]
[ 2, 5, 7 ]
[ 5, 1, 4, 2 ] - [ 5, 7, 2 ]
Cartan matrix
(1 1 1 1 0 0 0)
(1 1 1 0 1 0 0)
(0 0 1 0 0 0 0)
(0 1 1 1 1 0 0)
(1 1 1 1 1 0 1)
(0 1 1 0 0 1 1)
(0 1 1 0 0 0 1)
Good mutations
vertex 1 -> Algebra 413 permutation [ 2, 3, 5, 4, 6, 7, 1 ]
vertex 2 -> Algebra 348 permutation [ 7, 1, 4, 2, 5, 3, 6 ]
vertex 3 -> Algebra 334 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 404 permutation [ 3, 2, 7, 6, 5, 1, 4 ]
vertex 6 -> Algebra 363 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 363
Quiver
[ 1, 4 ], [ 2, 3 ], [ 2, 5 ], [ 4, 2 ], [ 5, 1 ], [ 5, 6 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 4, 2, 5, 1 ]
[ 2, 5, 1, 4 ]
[ 1, 4, 2, 5 ]
[ 6, 2, 5 ]
[ 2, 5, 6 ]
[ 5, 1, 4, 2 ] - [ 5, 6, 2 ]
Cartan matrix
(1 1 1 1 0 0 0)
(1 1 1 0 1 0 0)
(0 0 1 0 0 0 0)
(0 1 1 1 1 0 0)
(1 1 1 1 1 1 1)
(0 1 1 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 411 permutation [ 3, 2, 5, 6, 7, 4, 1 ]
vertex 2 -> Algebra 293 permutation [ 1, 4, 5, 2, 3, 6, 7 ]
vertex 3 -> Algebra 276 permutation [ 1, 4, 3, 5, 2, 6, 7 ]
vertex 4 -> Algebra 310 permutation [ 3, 2, 5, 6, 7, 1, 4 ]
vertex 7 -> Algebra 362 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 364
Quiver
[ 1, 2 ], [ 1, 5 ], [ 2, 4 ], [ 3, 5 ], [ 4, 1 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 2, 4, 1 ]
[ 5, 4, 1 ]
[ 4, 1, 2 ]
[ 6, 5, 4 ]
[ 5, 4, 6 ]
[ 1, 2, 4 ] - [ 1, 5, 4 ]
[ 4, 1, 5 ] - [ 4, 6, 5 ]
Cartan matrix
(1 1 0 1 1 0 0)
(0 1 0 1 0 1 1)
(0 0 1 1 1 0 0)
(1 0 0 1 1 1 1)
(0 0 0 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 256 permutation [ 3, 5, 4, 6, 7, 1, 2 ]
vertex 2 -> Algebra 276 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 411 permutation [ 3, 5, 4, 6, 7, 1, 2 ]
vertex 5 -> Algebra 216 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 402 permutation [ 3, 5, 4, 1, 7, 6, 2 ]
Algebra 366
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 2, 4, 5, 1 ]
[ 4, 5, 1, 2 ]
[ 4, 5, 3 ]
[ 1, 2, 4, 5 ]
[ 3, 4, 5 ]
[ 5, 1, 2, 4 ] - [ 5, 3, 4 ]
Cartan matrix
(1 1 0 1 0 0 0)
(0 1 0 1 1 1 0)
(0 0 1 1 0 0 0)
(1 0 0 1 1 1 0)
(1 1 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 219 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 278 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 402 permutation [ 3, 5, 4, 1, 7, 6, 2 ]
vertex 6 -> Algebra 391 permutation [ 5, 1, 2, 3, 4, 6, 7 ]
vertex 7 -> Algebra 216 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 367
Quiver
[ 1, 6 ], [ 2, 5 ], [ 3, 1 ], [ 4, 6 ], [ 5, 3 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3, 1 ]
[ 1, 6, 5, 3 ]
[ 6, 5, 4 ]
[ 3, 1, 6, 5 ]
[ 4, 6, 5 ]
[ 5, 3, 1, 6 ] - [ 5, 4, 6 ]
Cartan matrix
(1 0 0 0 1 1 1)
(1 1 1 1 1 1 1)
(1 0 1 0 0 1 1)
(0 0 0 1 0 1 1)
(1 0 1 1 1 1 1)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 410 permutation [ 1, 3, 4, 6, 7, 5, 2 ]
vertex 2 -> Algebra 372 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 3 -> Algebra 217 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 238 permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex 6 -> Algebra 407 permutation [ 3, 1, 2, 6, 5, 7, 4 ]
vertex 7 -> Algebra 412 permutation [ 1, 6, 2, 5, 4, 3, 7 ]
Algebra 369
Quiver
[ 1, 3 ], [ 1, 6 ], [ 2, 5 ], [ 3, 5 ], [ 4, 6 ], [ 5, 1 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 3, 5, 1 ]
[ 6, 5, 1 ]
[ 5, 1, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 1, 3, 5 ] - [ 1, 6, 5 ]
[ 5, 1, 6 ] - [ 5, 4, 6 ]
Cartan matrix
(1 0 1 0 1 1 0)
(1 1 0 1 1 1 0)
(0 0 1 1 1 0 0)
(0 0 0 1 0 1 0)
(1 0 0 1 1 1 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 375 permutation [ 3, 1, 6, 7, 4, 5, 2 ]
vertex 2 -> Algebra 373 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 3 -> Algebra 412 permutation [ 1, 6, 2, 5, 4, 3, 7 ]
vertex 4 -> Algebra 315 permutation [ 3, 5, 1, 4, 7, 6, 2 ]
vertex 5 -> Algebra 219 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 409 permutation [ 1, 3, 2, 6, 4, 5, 7 ]
vertex 7 -> Algebra 217 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 371
Quiver
[ 1, 5 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 5, 2, 1 ]
[ 1, 5, 2 ]
[ 4, 5, 2 ]
[ 4, 5, 3 ]
[ 3, 4, 5 ]
[ 5, 2, 4 ] - [ 5, 3, 4 ]
[ 2, 1, 5 ] - [ 2, 4, 5 ]
Cartan matrix
(1 0 1 0 1 0 0)
(1 1 0 1 1 0 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 0 0)
(0 1 1 1 1 0 0)
(0 1 1 1 1 1 1)
(0 1 1 1 1 0 1)
Good mutations
vertex 1 -> Algebra 408 permutation [ 3, 4, 6, 1, 7, 5, 2 ]
vertex 2 -> Algebra 225 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 308 permutation [ 1, 5, 2, 3, 4, 7, 6 ]
vertex 4 -> Algebra 358 permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex 5 -> Algebra 410 permutation [ 1, 3, 2, 5, 4, 7, 6 ]
vertex 6 -> Algebra 307 permutation [ 1, 5, 2, 3, 4, 7, 6 ]
Algebra 372
Quiver
[ 1, 6 ], [ 2, 3 ], [ 2, 4 ], [ 2, 5 ], [ 3, 1 ], [ 4, 6 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 6, 2, 3, 1 ]
[ 3, 1, 6, 2 ]
[ 4, 6, 2 ]
[ 1, 6, 2, 3 ]
[ 6, 2, 4 ]
[ 2, 3, 1, 6 ] - [ 2, 4, 6 ]
Cartan matrix
(1 1 0 0 1 1 1)
(1 1 1 1 1 1 1)
(1 0 1 0 0 1 1)
(0 0 0 1 0 1 1)
(0 0 0 0 1 0 0)
(0 1 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 309 permutation [ 1, 3, 4, 6, 7, 2, 5 ]
vertex 2 -> Algebra 373 permutation [ 3, 6, 1, 5, 7, 2, 4 ]
vertex 3 -> Algebra 220 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 367 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 6 -> Algebra 393 permutation [ 3, 6, 4, 1, 7, 2, 5 ]
vertex 7 -> Algebra 409 permutation [ 3, 1, 7, 2, 5, 6, 4 ]
Algebra 373
Quiver
[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 4 ], [ 2, 5 ], [ 3, 2 ], [ 4, 6 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 3, 2, 1 ]
[ 6, 2, 1 ]
[ 4, 6, 2 ]
[ 2, 1, 3 ]
[ 6, 2, 4 ]
[ 1, 3, 2 ] - [ 1, 6, 2 ]
[ 2, 1, 6 ] - [ 2, 4, 6 ]
Cartan matrix
(1 1 1 0 1 1 0)
(1 1 0 1 1 1 0)
(0 1 1 1 1 0 0)
(0 0 0 1 0 1 0)
(0 0 0 0 1 0 0)
(0 1 0 0 1 1 0)
(0 1 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 221 permutation [ 3, 1, 6, 7, 4, 2, 5 ]
vertex 2 -> Algebra 223 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 409 permutation [ 3, 1, 7, 2, 5, 6, 4 ]
vertex 4 -> Algebra 241 permutation [ 3, 1, 7, 4, 6, 2, 5 ]
vertex 5 -> Algebra 369 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 6 -> Algebra 372 permutation [ 3, 6, 1, 7, 4, 2, 5 ]
vertex 7 -> Algebra 220 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 374
Quiver
[ 1, 2 ], [ 2, 5 ], [ 2, 7 ], [ 3, 2 ], [ 4, 3 ], [ 5, 3 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 7, 6, 2 ]
[ 2, 5, 3 ]
[ 3, 2, 5 ]
[ 6, 2, 5 ]
[ 6, 2, 7 ]
[ 5, 3, 2 ] - [ 5, 6, 2 ]
[ 2, 5, 6 ] - [ 2, 7, 6 ]
Cartan matrix
(1 1 0 0 1 1 1)
(0 1 0 0 1 1 1)
(0 1 1 0 0 0 1)
(0 1 1 1 0 0 1)
(0 1 1 0 1 1 0)
(0 1 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 404 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 281 permutation [ 6, 2, 1, 5, 7, 3, 4 ]
vertex 4 -> Algebra 255 permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex 5 -> Algebra 331 permutation [ 6, 1, 2, 7, 5, 4, 3 ]
vertex 6 -> Algebra 221 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 334 permutation [ 6, 1, 2, 7, 5, 4, 3 ]
Algebra 375
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 2 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 3, 2 ]
[ 2, 6, 5, 3 ]
[ 3, 2, 6, 5 ]
[ 5, 3, 2, 6 ]
Cartan matrix
(1 1 0 0 1 1 0)
(0 1 0 0 1 1 0)
(0 1 1 0 0 1 0)
(0 1 1 1 0 1 0)
(0 1 1 0 1 0 0)
(0 0 1 0 1 1 0)
(0 0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 405 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 369 permutation [ 2, 7, 1, 5, 6, 3, 4 ]
vertex 3 -> Algebra 223 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 256 permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex 6 -> Algebra 402 permutation [ 1, 2, 5, 6, 4, 3, 7 ]
vertex 7 -> Algebra 221 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 377
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 6 ], [ 6, 2 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 4, 2, 3 ]
[ 5, 6, 2, 3 ]
[ 2, 3, 4 ]
[ 2, 3, 5, 6 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
[ 3, 4, 2 ] - [ 3, 5, 6, 2 ]
[ 6, 2, 3, 5 ] - [ 6, 7, 5 ]
Cartan matrix
(1 1 1 0 1 0 0)
(0 1 1 0 1 0 0)
(0 1 1 1 1 1 0)
(0 1 0 1 0 0 0)
(0 1 0 0 1 1 0)
(0 1 1 0 1 1 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 406 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 393 permutation [ 1, 6, 7, 3, 5, 2, 4 ]
vertex 3 -> Algebra 402 permutation [ 1, 2, 5, 6, 4, 3, 7 ]
vertex 5 -> Algebra 265 permutation [ 1, 2, 3, 6, 4, 5, 7 ]
vertex 6 -> Algebra 223 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 379
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 4, 1 ], [ 4, 3 ], [ 5, 4 ], [ 6, 1 ], [ 7, 6 ]
Relations
[ 2, 5, 4, 1 ]
[ 5, 4, 1, 2 ]
[ 5, 4, 3 ]
[ 1, 2, 5, 4 ]
[ 3, 5, 4 ]
[ 4, 1, 2, 5 ] - [ 4, 3, 5 ]
Cartan matrix
(1 1 0 0 1 0 0)
(0 1 0 1 1 0 0)
(0 0 1 0 1 0 0)
(1 1 1 1 1 0 0)
(1 0 0 1 1 0 0)
(1 1 0 0 1 1 0)
(1 1 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 230 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 286 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 227 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 391
Quiver
[ 1, 2 ], [ 1, 4 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 1 ], [ 6, 1 ], [ 6, 7 ]
Relations
[ 2, 3, 5, 1 ]
[ 4, 5, 1 ]
[ 3, 5, 1, 2 ]
[ 5, 1, 2, 3 ]
[ 5, 1, 4 ]
[ 1, 2, 3, 5 ] - [ 1, 4, 5 ]
Cartan matrix
(1 1 1 1 1 0 0)
(0 1 1 0 1 0 0)
(1 0 1 0 1 0 0)
(0 0 0 1 1 0 0)
(1 1 0 0 1 0 0)
(1 1 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 393 permutation [ 4, 2, 3, 1, 5, 6, 7 ]
vertex 2 -> Algebra 307 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 343 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 6 -> Algebra 366 permutation [ 2, 3, 4, 5, 1, 6, 7 ]
vertex 7 -> Algebra 408 permutation [ 4, 5, 7, 2, 6, 1, 3 ]
Algebra 393
Quiver
[ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 5 ], [ 4, 6 ], [ 5, 2 ], [ 6, 1 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 4, 6, 1 ]
[ 3, 5, 2 ]
[ 5, 2, 3 ]
[ 5, 2, 4 ]
[ 1, 4, 6 ]
[ 2, 4, 6 ]
[ 4, 5, 2 ] - [ 4, 6, 2 ]
[ 6, 1, 4 ] - [ 6, 2, 4 ]
[ 2, 3, 5 ] - [ 2, 4, 5 ]
Cartan matrix
(1 0 0 1 1 0 0)
(0 1 1 1 1 0 0)
(0 0 1 0 1 0 0)
(0 1 0 1 1 1 1)
(0 1 0 0 1 0 0)
(1 1 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 372 permutation [ 4, 6, 1, 3, 7, 2, 5 ]
vertex 4 -> Algebra 391 permutation [ 4, 2, 3, 1, 5, 6, 7 ]
vertex 5 -> Algebra 301 permutation [ 1, 4, 6, 2, 7, 5, 3 ]
vertex 6 -> Algebra 377 permutation [ 1, 6, 4, 7, 5, 2, 3 ]
vertex 7 -> Algebra 407 permutation [ 1, 4, 7, 2, 6, 5, 3 ]
Algebra 402
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 4, 7 ], [ 5, 6 ], [ 6, 2 ], [ 7, 3 ]
Relations
[ 6, 2, 3 ]
[ 2, 3, 4 ]
[ 7, 3, 4 ]
[ 2, 3, 6 ]
[ 3, 4, 7 ]
[ 3, 4, 2 ] - [ 3, 6, 2 ]
[ 4, 2, 3 ] - [ 4, 7, 3 ]
Cartan matrix
(1 1 1 0 0 0 0)
(0 1 1 0 0 0 0)
(0 1 1 1 0 1 0)
(0 1 1 1 0 0 1)
(0 1 0 0 1 1 0)
(0 1 0 0 0 1 0)
(0 0 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 413 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 366 permutation [ 4, 7, 1, 3, 2, 6, 5 ]
vertex 4 -> Algebra 375 permutation [ 1, 2, 6, 5, 3, 4, 7 ]
vertex 5 -> Algebra 364 permutation [ 4, 7, 1, 3, 2, 6, 5 ]
vertex 6 -> Algebra 377 permutation [ 1, 2, 6, 5, 3, 4, 7 ]
vertex 7 -> Algebra 334 permutation [ 7, 1, 2, 4, 3, 5, 6 ]
Algebra 403
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 6 ], [ 4, 3 ], [ 5, 3 ], [ 6, 2 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 2, 3, 1 ]
[ 1, 2, 3 ]
[ 3, 6, 5 ]
[ 2, 3, 6 ]
[ 5, 3, 6 ]
[ 3, 1, 2 ] - [ 3, 6, 2 ]
[ 6, 2, 3 ] - [ 6, 5, 3 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 1 0 0 0 0)
(1 1 1 0 0 1 1)
(1 1 1 1 0 1 1)
(1 0 1 0 1 0 0)
(0 1 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 409 permutation [ 2, 1, 4, 6, 7, 3, 5 ]
vertex 2 -> Algebra 279 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 310 permutation [ 2, 3, 4, 6, 7, 1, 5 ]
vertex 4 -> Algebra 309 permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex 5 -> Algebra 296 permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex 6 -> Algebra 412 permutation [ 2, 6, 4, 3, 7, 1, 5 ]
vertex 7 -> Algebra 415 permutation [ 6, 1, 2, 5, 4, 3, 7 ]
Algebra 404
Quiver
[ 2, 1 ], [ 2, 5 ], [ 2, 7 ], [ 3, 2 ], [ 4, 3 ], [ 5, 3 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 7, 6, 2 ]
[ 2, 5, 3 ]
[ 3, 2, 5 ]
[ 6, 2, 5 ]
[ 6, 2, 7 ]
[ 5, 3, 2 ] - [ 5, 6, 2 ]
[ 2, 5, 6 ] - [ 2, 7, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 1 1 1)
(1 1 1 0 0 0 1)
(1 1 1 1 0 0 1)
(1 1 1 0 1 1 0)
(1 1 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 374 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 415 permutation [ 3, 6, 1, 7, 5, 2, 4 ]
vertex 4 -> Algebra 310 permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex 5 -> Algebra 358 permutation [ 6, 2, 1, 7, 5, 4, 3 ]
vertex 6 -> Algebra 279 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 362 permutation [ 6, 2, 1, 7, 5, 4, 3 ]
Algebra 405
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 2 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 3, 2 ]
[ 2, 6, 5, 3 ]
[ 3, 2, 6, 5 ]
[ 5, 3, 2, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 1 1 0)
(1 1 1 0 0 1 0)
(1 1 1 1 0 1 0)
(1 1 1 0 1 0 0)
(0 0 1 0 1 1 0)
(0 0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 375 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 415 permutation [ 6, 1, 2, 5, 4, 3, 7 ]
vertex 3 -> Algebra 281 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 311 permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex 6 -> Algebra 413 permutation [ 2, 1, 5, 6, 4, 3, 7 ]
vertex 7 -> Algebra 279 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 406
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 6 ], [ 6, 2 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 4, 2, 3 ]
[ 5, 6, 2, 3 ]
[ 2, 3, 4 ]
[ 2, 3, 5, 6 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
[ 3, 4, 2 ] - [ 3, 5, 6, 2 ]
[ 6, 2, 3, 5 ] - [ 6, 7, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 0 0)
(1 1 1 1 1 1 0)
(1 1 0 1 0 0 0)
(1 1 0 0 1 1 0)
(1 1 1 0 1 1 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 377 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 413 permutation [ 2, 1, 5, 6, 4, 3, 7 ]
vertex 5 -> Algebra 320 permutation [ 2, 1, 3, 6, 4, 5, 7 ]
vertex 6 -> Algebra 281 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 407
Quiver
[ 1, 2 ], [ 2, 5 ], [ 2, 6 ], [ 3, 5 ], [ 4, 2 ], [ 4, 7 ], [ 5, 1 ], [ 5, 4 ], [ 6, 4 ], [ 7, 6 ]
Relations
[ 2, 5, 1 ]
[ 6, 4, 2 ]
[ 7, 6, 4 ]
[ 1, 2, 5 ]
[ 4, 2, 5 ]
[ 6, 4, 7 ]
[ 5, 1, 2 ] - [ 5, 4, 2 ]
[ 2, 5, 4 ] - [ 2, 6, 4 ]
[ 4, 2, 6 ] - [ 4, 7, 6 ]
Cartan matrix
(1 1 0 0 0 1 0)
(0 1 0 1 1 1 0)
(1 1 1 1 1 1 1)
(0 1 0 1 0 1 1)
(1 1 0 1 1 1 1)
(0 0 0 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 408 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex 3 -> Algebra 393 permutation [ 1, 4, 7, 2, 6, 5, 3 ]
vertex 4 -> Algebra 367 permutation [ 2, 3, 1, 7, 5, 4, 6 ]
vertex 6 -> Algebra 296 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 408
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 5 ], [ 4, 7 ], [ 5, 6 ], [ 6, 1 ], [ 6, 4 ], [ 7, 2 ]
Relations
[ 2, 6, 1 ]
[ 7, 2, 6, 4 ]
[ 1, 2, 6 ]
[ 4, 7, 2, 6 ]
[ 2, 6, 4, 7 ]
[ 6, 1, 2 ] - [ 6, 4, 7, 2 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 1 0 1 0)
(1 1 1 1 1 1 1)
(0 1 0 1 0 0 1)
(1 1 0 1 1 1 1)
(1 1 0 1 0 1 1)
(0 1 0 0 0 1 1)
Good mutations
vertex 3 -> Algebra 391 permutation [ 6, 4, 7, 1, 2, 5, 3 ]
vertex 4 -> Algebra 371 permutation [ 4, 7, 1, 2, 6, 3, 5 ]
vertex 6 -> Algebra 407 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex 7 -> Algebra 354 permutation [ 7, 1, 2, 4, 3, 5, 6 ]
Algebra 409
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 6 ], [ 4, 1 ], [ 4, 5 ], [ 4, 7 ], [ 6, 4 ], [ 7, 6 ]
Relations
[ 2, 6, 4, 1 ]
[ 6, 4, 1, 2 ]
[ 1, 2, 6, 4 ]
[ 7, 6, 4 ]
[ 6, 4, 7 ]
[ 4, 1, 2, 6 ] - [ 4, 7, 6 ]
Cartan matrix
(1 1 0 0 0 1 0)
(0 1 0 1 1 1 0)
(1 0 1 1 1 1 0)
(1 1 0 1 1 1 1)
(0 0 0 0 1 0 0)
(1 0 0 1 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 373 permutation [ 2, 4, 1, 7, 5, 6, 3 ]
vertex 2 -> Algebra 403 permutation [ 2, 1, 6, 3, 7, 4, 5 ]
vertex 3 -> Algebra 372 permutation [ 2, 4, 1, 7, 5, 6, 3 ]
vertex 4 -> Algebra 369 permutation [ 1, 3, 2, 5, 6, 4, 7 ]
vertex 5 -> Algebra 412 permutation [ 2, 6, 5, 4, 7, 1, 3 ]
vertex 6 -> Algebra 309 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 410
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 4, 6 ], [ 6, 2 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 2, 4, 1 ]
[ 4, 6, 3 ]
[ 1, 2, 4 ]
[ 2, 4, 6 ]
[ 3, 4, 6 ]
[ 4, 1, 2 ] - [ 4, 6, 2 ]
[ 6, 2, 4 ] - [ 6, 3, 4 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 1 1 0 0)
(1 0 1 1 1 0 0)
(1 1 0 1 1 1 0)
(0 0 0 0 1 0 0)
(0 1 1 1 1 1 0)
(0 1 1 1 1 1 1)
Good mutations
vertex 1 -> Algebra 367 permutation [ 1, 7, 2, 3, 6, 4, 5 ]
vertex 2 -> Algebra 311 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 355 permutation [ 6, 1, 2, 3, 4, 5, 7 ]
vertex 4 -> Algebra 371 permutation [ 1, 3, 2, 5, 4, 7, 6 ]
vertex 5 -> Algebra 415 permutation [ 6, 1, 2, 3, 5, 4, 7 ]
vertex 7 -> Algebra 309 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 411
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 4, 5 ], [ 6, 2 ], [ 6, 7 ], [ 7, 3 ]
Relations
[ 4, 2, 3 ]
[ 2, 3, 4 ]
[ 2, 3, 6 ]
[ 7, 3, 6 ]
[ 3, 6, 7 ]
[ 3, 4, 2 ] - [ 3, 6, 2 ]
[ 6, 2, 3 ] - [ 6, 7, 3 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 0 0 0)
(1 1 1 1 1 1 0)
(1 1 0 1 1 0 0)
(0 0 0 0 1 0 0)
(1 1 1 0 0 1 1)
(0 0 1 1 1 0 1)
Good mutations
vertex 1 -> Algebra 364 permutation [ 6, 7, 1, 3, 2, 4, 5 ]
vertex 5 -> Algebra 413 permutation [ 2, 1, 3, 6, 5, 4, 7 ]
vertex 6 -> Algebra 311 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 363 permutation [ 7, 2, 1, 6, 3, 4, 5 ]
Algebra 412
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 2 ], [ 6, 1 ], [ 7, 2 ]
Relations
[ 2, 4, 6, 1 ]
[ 5, 2, 4 ]
[ 6, 1, 2, 4 ]
[ 2, 4, 5 ]
[ 1, 2, 4, 6 ]
[ 4, 5, 2 ] - [ 4, 6, 1, 2 ]
Cartan matrix
(1 1 0 1 0 0 0)
(0 1 0 1 0 1 0)
(1 1 1 1 1 1 0)
(1 1 0 1 1 1 0)
(0 1 0 0 1 0 0)
(1 1 0 0 0 1 0)
(0 1 0 1 0 1 1)
Good mutations
vertex 1 -> Algebra 415 permutation [ 4, 1, 6, 5, 7, 2, 3 ]
vertex 2 -> Algebra 403 permutation [ 6, 1, 4, 3, 7, 2, 5 ]
vertex 3 -> Algebra 409 permutation [ 6, 1, 7, 4, 3, 2, 5 ]
vertex 4 -> Algebra 312 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 369 permutation [ 1, 3, 6, 5, 4, 2, 7 ]
vertex 7 -> Algebra 367 permutation [ 1, 3, 6, 5, 4, 2, 7 ]
Algebra 413
Quiver
[ 1, 2 ], [ 1, 3 ], [ 3, 4 ], [ 3, 6 ], [ 4, 1 ], [ 4, 7 ], [ 5, 6 ], [ 6, 1 ], [ 7, 3 ]
Relations
[ 6, 1, 3 ]
[ 1, 3, 4 ]
[ 7, 3, 4 ]
[ 1, 3, 6 ]
[ 3, 4, 7 ]
[ 3, 4, 1 ] - [ 3, 6, 1 ]
[ 4, 1, 3 ] - [ 4, 7, 3 ]
Cartan matrix
(1 1 1 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 1 0 1 0)
(1 1 1 1 0 0 1)
(1 1 0 0 1 1 0)
(1 1 0 0 0 1 0)
(0 0 1 0 0 1 1)
Good mutations
vertex 2 -> Algebra 402 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 405 permutation [ 2, 1, 6, 5, 3, 4, 7 ]
vertex 5 -> Algebra 411 permutation [ 2, 1, 3, 6, 5, 4, 7 ]
vertex 6 -> Algebra 406 permutation [ 2, 1, 6, 5, 3, 4, 7 ]
vertex 7 -> Algebra 362 permutation [ 7, 1, 2, 4, 3, 5, 6 ]
Algebra 415
Quiver
[ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 3, 6 ], [ 4, 6 ], [ 5, 6 ], [ 6, 1 ], [ 6, 2 ], [ 7, 1 ]
Relations
[ 3, 6, 1 ]
[ 4, 6, 1 ]
[ 3, 6, 2 ]
[ 6, 1, 4 ]
[ 2, 3, 6 ]
[ 6, 1, 3 ] - [ 6, 2, 3 ]
[ 1, 3, 6 ] - [ 1, 4, 6 ]
Cartan matrix
(1 0 1 1 0 1 0)
(0 1 1 0 0 0 0)
(0 0 1 0 0 1 0)
(0 1 0 1 0 1 0)
(1 1 1 0 1 1 0)
(1 1 1 0 0 1 0)
(1 0 1 1 0 1 1)
Good mutations
vertex 2 -> Algebra 412 permutation [ 2, 6, 7, 1, 4, 3, 5 ]
vertex 3 -> Algebra 405 permutation [ 2, 3, 6, 5, 4, 1, 7 ]
vertex 4 -> Algebra 351 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 410 permutation [ 2, 3, 4, 6, 5, 1, 7 ]
vertex 6 -> Algebra 404 permutation [ 3, 6, 1, 7, 5, 2, 4 ]
vertex 7 -> Algebra 403 permutation [ 2, 3, 6, 5, 4, 1, 7 ]