Algebra 6
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 1 1 0 1 1)
(0 1 1 1 0 1 1)
(0 0 1 1 0 1 1)
(0 0 0 1 0 0 0)
(0 0 1 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 12 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 27 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 31 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 32 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 7
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 1 1 1 0 1)
(0 1 1 1 1 0 1)
(0 0 1 1 1 0 1)
(0 0 0 1 0 0 0)
(0 0 0 0 1 0 1)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 13 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 28 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 33 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 12
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 1 1)
(0 0 1 1 0 1 1)
(0 0 0 1 0 0 0)
(0 0 1 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 6 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 38 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 47 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 51 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 52 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 13
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 1 0 1)
(0 0 1 1 1 0 1)
(0 0 0 1 0 0 0)
(0 0 0 0 1 0 1)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 7 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 39 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 48 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 53 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 26
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 5, 3, 2 ]
[ 2, 5, 3 ]
[ 4, 5, 3 ]
[ 5, 3, 4 ]
[ 3, 2, 5 ] - [ 3, 4, 5 ]
Cartan matrix
(1 1 0 0 1 1 1)
(0 1 0 0 1 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 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 46 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 92 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 94 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 27
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 6 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 1 0 0 1 1)
(0 1 1 0 0 1 1)
(0 0 1 0 0 1 1)
(0 0 1 1 0 1 1)
(0 0 1 0 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 47 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 95 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 6 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 96 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 97 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 28
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 1 0 1 0 1)
(0 1 1 0 1 0 1)
(0 0 1 0 1 0 1)
(0 0 1 1 1 0 1)
(0 0 0 0 1 0 1)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 48 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 7 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 98 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 31
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 7 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 1 1 1 0 0 1)
(0 1 1 1 0 0 1)
(0 0 1 1 0 0 1)
(0 0 0 1 0 0 0)
(0 0 1 1 1 1 0)
(0 0 1 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 51 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 96 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 33 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 6 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 32
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 1 1 0 1 0)
(0 1 1 1 0 1 0)
(0 0 1 1 0 1 0)
(0 0 0 1 0 0 0)
(0 0 1 1 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 52 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 97 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 107 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 6 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 33
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 7 ], [ 5, 3 ], [ 5, 6 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 3, 7, 5 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 1 1 0 0 1)
(0 1 1 1 0 0 1)
(0 0 1 1 0 0 1)
(0 0 0 1 0 0 0)
(0 0 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 53 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 98 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 7 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 31 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 38
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 6 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 1 0 1 1)
(0 0 0 1 0 0 0)
(0 1 1 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 58 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 12 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 118 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 115 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 119 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 120 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 39
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 1 1 0 1)
(0 0 0 1 0 0 0)
(0 0 0 0 1 0 1)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 59 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 13 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 112 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 116 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 121 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 46
Quiver
[ 2, 1 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 5, 3, 2 ]
[ 2, 5, 3 ]
[ 4, 5, 3 ]
[ 5, 3, 4 ]
[ 3, 2, 5 ] - [ 3, 4, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 1 1 1)
(1 1 1 1 1 1 1)
(0 0 0 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 26 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 139 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 141 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 47
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 6 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 0 1 1)
(0 0 1 0 0 1 1)
(0 0 1 1 0 1 1)
(0 0 1 0 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 27 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 115 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 142 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 12 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 143 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 144 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 48
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 0 1)
(0 0 1 0 1 0 1)
(0 0 1 1 1 0 1)
(0 0 0 0 1 0 1)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 28 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 116 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 13 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 145 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 51
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 7 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 0 1)
(0 0 1 1 0 0 1)
(0 0 0 1 0 0 0)
(0 0 1 1 1 1 0)
(0 0 1 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 31 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 119 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 143 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 53 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 12 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 52
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 1 0)
(0 0 1 1 0 1 0)
(0 0 0 1 0 0 0)
(0 0 1 1 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 32 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 120 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 144 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 154 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 12 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 53
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 7 ], [ 5, 3 ], [ 5, 6 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 3, 7, 5 ]
[ 5, 3, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 0 1)
(0 0 1 1 0 0 1)
(0 0 0 1 0 0 0)
(0 0 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 33 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 121 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 145 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 13 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 51 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 58
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 3, 6 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 1 0 1 1)
(0 0 0 1 0 0 0)
(1 1 1 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 38 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 165 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 162 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 166 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 167 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 59
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 3, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 1 1 0 1)
(0 0 0 1 0 0 0)
(0 0 0 0 1 0 1)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 39 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 159 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 163 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 168 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 92
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 5 ], [ 4, 6 ], [ 5, 2 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 2 ]
[ 6, 5, 4 ]
[ 2, 6, 5 ]
[ 4, 6, 5 ]
[ 5, 2, 6 ] - [ 5, 4, 6 ]
Cartan matrix
(1 1 0 0 0 1 1)
(0 1 0 0 0 1 1)
(0 1 1 1 1 1 1)
(0 0 0 1 0 1 1)
(0 1 0 1 1 1 1)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 139 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 95 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 5 -> Algebra 26 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 242 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 243 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 94
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 5, 3, 2 ]
[ 2, 5, 3 ]
[ 4, 5, 3 ]
[ 5, 3, 4 ]
[ 3, 2, 5 ] - [ 3, 4, 5 ]
Cartan matrix
(1 1 0 0 1 1 0)
(0 1 0 0 1 1 0)
(0 1 1 1 1 1 0)
(0 0 0 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 141 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 243 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 118 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 7 -> Algebra 26 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 95
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 4, 6 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 6, 3, 2 ]
[ 2, 6, 3 ]
[ 4, 6, 3 ]
[ 6, 3, 4 ]
[ 3, 2, 6 ] - [ 3, 4, 6 ]
Cartan matrix
(1 1 0 0 0 1 1)
(0 1 0 0 0 1 1)
(0 1 1 1 1 1 1)
(0 0 0 1 0 1 1)
(0 0 0 0 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 142 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 27 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 92 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 246 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 247 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 96
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 7 ], [ 4, 3 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 1 1 0 0 0 1)
(0 1 1 0 0 0 1)
(0 0 1 0 0 0 1)
(0 0 1 1 0 0 1)
(0 0 1 0 1 1 0)
(0 0 1 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 143 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 248 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 31 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 98 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 27 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 97
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 6 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 1 0 0 1 0)
(0 1 1 0 0 1 0)
(0 0 1 0 0 1 0)
(0 0 1 1 0 1 0)
(0 0 1 0 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 144 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 247 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 32 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 112 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 27 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 98
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 7 ], [ 4, 3 ], [ 5, 3 ], [ 5, 6 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 3, 7, 5 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 1 0 0 0 1)
(0 1 1 0 0 0 1)
(0 0 1 0 0 0 1)
(0 0 1 1 0 0 1)
(0 0 1 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 145 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 175 permutation [ 4, 1, 2, 7, 3, 5, 6 ]
vertex 4 -> Algebra 33 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 28 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 96 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 107
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 5, 6 ], [ 6, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
Cartan matrix
(1 1 1 1 0 0 0)
(0 1 1 1 0 0 0)
(0 0 1 1 0 0 0)
(0 0 0 1 0 0 0)
(0 0 1 1 1 1 0)
(0 0 1 1 0 1 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 154 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 112 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 32 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 112
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 3 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 1 0 0 0 0)
(0 1 1 0 0 0 0)
(0 0 1 0 0 0 0)
(0 0 1 1 0 0 0)
(0 0 1 0 1 0 1)
(0 0 1 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 159 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 39 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 107 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 5 -> Algebra 97 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 115
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 6 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 0 0 1 1)
(0 1 1 1 0 1 1)
(0 1 1 0 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 162 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 47 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 38 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 266 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 267 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 116
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 0 1 0 1)
(0 1 1 1 1 0 1)
(0 0 0 0 1 0 1)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 163 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 48 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 39 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 268 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 118
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 3, 5, 2 ]
[ 3, 5, 4 ]
[ 2, 3, 5 ]
[ 4, 3, 5 ]
[ 5, 2, 3 ] - [ 5, 4, 3 ]
Cartan matrix
(1 1 1 0 0 0 0)
(0 1 1 0 0 0 0)
(0 0 1 0 1 0 0)
(0 0 1 1 0 0 0)
(0 1 1 1 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 165 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 38 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 94 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 7 -> Algebra 245 permutation [ 1, 2, 5, 4, 3, 7, 6 ]
Algebra 119
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 7 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 1 0 0 1)
(0 0 0 1 0 0 0)
(0 1 1 1 1 1 0)
(0 1 1 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 166 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 51 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 243 permutation [ 1, 2, 5, 4, 6, 3, 7 ]
vertex 4 -> Algebra 266 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 121 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 38 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 120
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 6 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 1 0 1 0)
(0 0 0 1 0 0 0)
(0 1 1 1 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 167 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 52 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 245 permutation [ 1, 2, 5, 4, 3, 7, 6 ]
vertex 4 -> Algebra 267 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 271 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 38 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 121
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 7 ], [ 5, 3 ], [ 5, 6 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 3, 7, 5 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 1 0 0 1)
(0 0 0 1 0 0 0)
(0 1 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 168 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 53 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 247 permutation [ 1, 2, 5, 4, 6, 3, 7 ]
vertex 4 -> Algebra 268 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 39 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 119 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 139
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 5 ], [ 4, 6 ], [ 5, 2 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 2 ]
[ 6, 5, 4 ]
[ 2, 6, 5 ]
[ 4, 6, 5 ]
[ 5, 2, 6 ] - [ 5, 4, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 0 1 1)
(1 1 1 1 1 1 1)
(0 0 0 1 0 1 1)
(1 1 0 1 1 1 1)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 92 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 142 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 5 -> Algebra 46 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 297 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 298 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 141
Quiver
[ 2, 1 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 5, 3, 2 ]
[ 2, 5, 3 ]
[ 4, 5, 3 ]
[ 5, 3, 4 ]
[ 3, 2, 5 ] - [ 3, 4, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 1 1 0)
(1 1 1 1 1 1 0)
(0 0 0 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 94 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 298 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 165 permutation [ 2, 1, 5, 4, 3, 6, 7 ]
vertex 7 -> Algebra 46 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 142
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 4, 6 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 6, 3, 2 ]
[ 2, 6, 3 ]
[ 4, 6, 3 ]
[ 6, 3, 4 ]
[ 3, 2, 6 ] - [ 3, 4, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 0 1 1)
(1 1 1 1 1 1 1)
(0 0 0 1 0 1 1)
(0 0 0 0 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 95 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 47 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 139 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 302 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 303 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 143
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 7 ], [ 4, 3 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 0 0 1)
(0 0 1 0 0 0 1)
(0 0 1 1 0 0 1)
(0 0 1 0 1 1 0)
(0 0 1 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 96 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 266 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 304 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 51 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 145 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 47 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 144
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 6 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 0 1 0)
(0 0 1 0 0 1 0)
(0 0 1 1 0 1 0)
(0 0 1 0 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 97 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 267 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 303 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 52 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 159 permutation [ 2, 1, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 47 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 145
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 7 ], [ 4, 3 ], [ 5, 3 ], [ 5, 6 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 3, 7, 5 ]
[ 5, 3, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 0 0 1)
(0 0 1 0 0 0 1)
(0 0 1 1 0 0 1)
(0 0 1 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 98 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 268 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 207 permutation [ 4, 2, 1, 7, 3, 5, 6 ]
vertex 4 -> Algebra 53 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 48 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 143 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 154
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 5, 6 ], [ 6, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 0 0 0)
(0 0 1 1 0 0 0)
(0 0 0 1 0 0 0)
(0 0 1 1 1 1 0)
(0 0 1 1 0 1 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 107 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 271 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 159 permutation [ 2, 1, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 52 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 159
Quiver
[ 1, 2 ], [ 1, 3 ], [ 4, 3 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 1 0 0 0 0)
(0 1 0 0 0 0 0)
(0 0 1 0 0 0 0)
(0 0 1 1 0 0 0)
(0 0 1 0 1 0 1)
(0 0 1 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 173 permutation [ 3, 2, 1, 4, 5, 6, 7 ]
vertex 2 -> Algebra 112 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 59 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 154 permutation [ 2, 1, 3, 4, 6, 5, 7 ]
vertex 5 -> Algebra 144 permutation [ 2, 1, 3, 4, 6, 5, 7 ]
Algebra 162
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 6 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 0 0 1 1)
(1 1 1 1 0 1 1)
(1 1 1 0 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 115 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 58 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 321 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 322 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 163
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 0 1 0 1)
(1 1 1 1 1 0 1)
(0 0 0 0 1 0 1)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 116 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 59 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 323 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 165
Quiver
[ 1, 2 ], [ 1, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 1 ], [ 5, 4 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 3, 5, 1 ]
[ 3, 5, 4 ]
[ 1, 3, 5 ]
[ 4, 3, 5 ]
[ 5, 1, 3 ] - [ 5, 4, 3 ]
Cartan matrix
(1 1 1 0 0 0 0)
(0 1 0 0 0 0 0)
(0 0 1 0 1 0 0)
(0 0 1 1 0 0 0)
(1 1 1 1 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 118 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 58 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 141 permutation [ 2, 1, 5, 4, 3, 6, 7 ]
vertex 7 -> Algebra 300 permutation [ 2, 1, 5, 4, 3, 7, 6 ]
Algebra 166
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 3, 7 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 1 0 0 1)
(0 0 0 1 0 0 0)
(1 1 1 1 1 1 0)
(1 1 1 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 119 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 298 permutation [ 2, 1, 5, 4, 6, 3, 7 ]
vertex 4 -> Algebra 321 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 168 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 58 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 167
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 3, 6 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 1 0 1 0)
(0 0 0 1 0 0 0)
(1 1 1 1 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 2 -> Algebra 120 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 300 permutation [ 2, 1, 5, 4, 3, 7, 6 ]
vertex 4 -> Algebra 322 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 326 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 58 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 168
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 3, 7 ], [ 5, 3 ], [ 5, 6 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 3, 7, 5 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 1 0 0 1)
(0 0 0 1 0 0 0)
(1 1 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 2 -> Algebra 121 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 303 permutation [ 2, 1, 5, 4, 6, 3, 7 ]
vertex 4 -> Algebra 323 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 59 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 166 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 173
Quiver
[ 1, 3 ], [ 2, 3 ], [ 4, 1 ], [ 5, 1 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 0 1 0 0 0 0)
(0 1 1 0 0 0 0)
(0 0 1 0 0 0 0)
(1 0 1 1 0 0 0)
(1 0 1 0 1 0 1)
(1 0 1 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 205 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 159 permutation [ 3, 2, 1, 4, 5, 6, 7 ]
vertex 4 -> Algebra 271 permutation [ 2, 3, 1, 4, 6, 5, 7 ]
vertex 5 -> Algebra 267 permutation [ 2, 3, 1, 4, 6, 5, 7 ]
Algebra 175
Quiver
[ 1, 4 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 4, 5, 1 ]
[ 4, 5, 3 ]
[ 1, 4, 5 ]
[ 3, 4, 5 ]
[ 5, 1, 4 ] - [ 5, 3, 4 ]
Cartan matrix
(1 0 0 1 0 0 0)
(0 1 1 1 0 0 0)
(0 0 1 1 0 0 0)
(0 0 0 1 1 1 1)
(1 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 207 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 5 -> Algebra 98 permutation [ 2, 3, 5, 1, 6, 7, 4 ]
vertex 7 -> Algebra 248 permutation [ 2, 3, 5, 1, 7, 6, 4 ]
Algebra 205
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 1 ], [ 5, 1 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 1 0 0 0 0)
(0 1 1 0 0 0 0)
(0 0 1 0 0 0 0)
(1 1 1 1 0 0 0)
(1 1 1 0 1 0 1)
(1 1 1 0 1 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 3 -> Algebra 173 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 326 permutation [ 2, 3, 1, 4, 6, 5, 7 ]
vertex 5 -> Algebra 322 permutation [ 2, 3, 1, 4, 6, 5, 7 ]
Algebra 207
Quiver
[ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 4, 5, 1 ]
[ 4, 5, 2 ]
[ 1, 4, 5 ]
[ 2, 4, 5 ]
[ 5, 1, 4 ] - [ 5, 2, 4 ]
Cartan matrix
(1 0 0 1 0 0 0)
(0 1 1 1 0 0 0)
(0 0 1 0 0 0 0)
(0 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 3 -> Algebra 175 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 5 -> Algebra 145 permutation [ 3, 2, 5, 1, 6, 7, 4 ]
vertex 7 -> Algebra 304 permutation [ 3, 2, 5, 1, 7, 6, 4 ]
Algebra 242
Quiver
[ 1, 2 ], [ 2, 7 ], [ 3, 5 ], [ 4, 7 ], [ 5, 6 ], [ 6, 2 ], [ 6, 4 ], [ 7, 6 ]
Relations
[ 7, 6, 2 ]
[ 7, 6, 4 ]
[ 2, 7, 6 ]
[ 4, 7, 6 ]
[ 6, 2, 7 ] - [ 6, 4, 7 ]
Cartan matrix
(1 1 0 0 0 0 1)
(0 1 0 0 0 0 1)
(0 1 1 1 1 1 1)
(0 0 0 1 0 0 1)
(0 1 0 1 1 1 1)
(0 1 0 1 0 1 1)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 297 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 246 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 92 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 243
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 5 ], [ 4, 6 ], [ 5, 2 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 2 ]
[ 6, 5, 4 ]
[ 2, 6, 5 ]
[ 4, 6, 5 ]
[ 5, 2, 6 ] - [ 5, 4, 6 ]
Cartan matrix
(1 1 0 0 0 1 0)
(0 1 0 0 0 1 0)
(0 1 1 1 1 1 0)
(0 0 0 1 0 1 0)
(0 1 0 1 1 1 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 298 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 247 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 5 -> Algebra 94 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 119 permutation [ 1, 2, 6, 4, 3, 5, 7 ]
vertex 7 -> Algebra 92 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 245
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 5, 3, 2 ]
[ 2, 5, 3 ]
[ 4, 5, 3 ]
[ 5, 3, 4 ]
[ 3, 2, 5 ] - [ 3, 4, 5 ]
Cartan matrix
(1 1 0 0 1 0 0)
(0 1 0 0 1 0 0)
(0 1 1 1 1 0 0)
(0 0 0 1 1 0 0)
(0 0 1 0 1 0 0)
(0 0 1 0 1 1 1)
(0 0 1 0 1 0 1)
Good mutations
vertex 1 -> Algebra 300 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 120 permutation [ 1, 2, 5, 4, 3, 7, 6 ]
vertex 6 -> Algebra 118 permutation [ 1, 2, 5, 4, 3, 7, 6 ]
Algebra 246
Quiver
[ 1, 2 ], [ 2, 7 ], [ 3, 5 ], [ 3, 6 ], [ 4, 7 ], [ 6, 2 ], [ 6, 4 ], [ 7, 6 ]
Relations
[ 7, 6, 2 ]
[ 7, 6, 4 ]
[ 2, 7, 6 ]
[ 4, 7, 6 ]
[ 6, 2, 7 ] - [ 6, 4, 7 ]
Cartan matrix
(1 1 0 0 0 0 1)
(0 1 0 0 0 0 1)
(0 1 1 1 1 1 1)
(0 0 0 1 0 0 1)
(0 0 0 0 1 0 0)
(0 1 0 1 0 1 1)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 302 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 248 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 5 -> Algebra 242 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 95 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 247
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 4, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 6, 3, 2 ]
[ 2, 6, 3 ]
[ 4, 6, 3 ]
[ 6, 3, 4 ]
[ 3, 2, 6 ] - [ 3, 4, 6 ]
Cartan matrix
(1 1 0 0 0 1 0)
(0 1 0 0 0 1 0)
(0 1 1 1 1 1 0)
(0 0 0 1 0 1 0)
(0 0 0 0 1 0 0)
(0 0 1 0 1 1 0)
(0 0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 303 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 97 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 243 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 121 permutation [ 1, 2, 6, 4, 3, 5, 7 ]
vertex 7 -> Algebra 95 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 248
Quiver
[ 1, 2 ], [ 2, 7 ], [ 3, 2 ], [ 3, 4 ], [ 3, 6 ], [ 4, 7 ], [ 5, 6 ], [ 7, 3 ]
Relations
[ 7, 3, 2 ]
[ 2, 7, 3 ]
[ 4, 7, 3 ]
[ 7, 3, 4 ]
[ 3, 2, 7 ] - [ 3, 4, 7 ]
Cartan matrix
(1 1 0 0 0 0 1)
(0 1 0 0 0 0 1)
(0 1 1 1 0 1 1)
(0 0 0 1 0 0 1)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 304 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 96 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 175 permutation [ 4, 1, 2, 7, 3, 6, 5 ]
vertex 6 -> Algebra 246 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
Algebra 266
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 7 ], [ 4, 3 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 0 0 0 1)
(0 1 1 1 0 0 1)
(0 1 1 0 1 1 0)
(0 1 1 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 321 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 143 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 119 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 268 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 115 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 267
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 6 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 0 0 1 0)
(0 1 1 1 0 1 0)
(0 1 1 0 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 322 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 144 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 120 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 173 permutation [ 3, 1, 2, 4, 6, 5, 7 ]
vertex 7 -> Algebra 115 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 268
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 7 ], [ 4, 3 ], [ 5, 3 ], [ 5, 6 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 3, 7, 5 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 0 0 0 1)
(0 1 1 1 0 0 1)
(0 1 1 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 323 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 145 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 121 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 116 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 266 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 271
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 5, 6 ], [ 6, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 1 0 0 0)
(0 0 0 1 0 0 0)
(0 1 1 1 1 1 0)
(0 1 1 1 0 1 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 326 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 154 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 173 permutation [ 3, 1, 2, 4, 6, 5, 7 ]
vertex 6 -> Algebra 120 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 297
Quiver
[ 2, 1 ], [ 2, 7 ], [ 3, 5 ], [ 4, 7 ], [ 5, 6 ], [ 6, 2 ], [ 6, 4 ], [ 7, 6 ]
Relations
[ 7, 6, 2 ]
[ 7, 6, 4 ]
[ 2, 7, 6 ]
[ 4, 7, 6 ]
[ 6, 2, 7 ] - [ 6, 4, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 0 0 1)
(1 1 1 1 1 1 1)
(0 0 0 1 0 0 1)
(1 1 0 1 1 1 1)
(1 1 0 1 0 1 1)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 242 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 302 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 139 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 298
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 5 ], [ 4, 6 ], [ 5, 2 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 2 ]
[ 6, 5, 4 ]
[ 2, 6, 5 ]
[ 4, 6, 5 ]
[ 5, 2, 6 ] - [ 5, 4, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 0 1 0)
(1 1 1 1 1 1 0)
(0 0 0 1 0 1 0)
(1 1 0 1 1 1 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 243 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 303 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 5 -> Algebra 141 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 166 permutation [ 2, 1, 6, 4, 3, 5, 7 ]
vertex 7 -> Algebra 139 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 300
Quiver
[ 2, 1 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 5, 3, 2 ]
[ 2, 5, 3 ]
[ 4, 5, 3 ]
[ 5, 3, 4 ]
[ 3, 2, 5 ] - [ 3, 4, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 1 0 0)
(1 1 1 1 1 0 0)
(0 0 0 1 1 0 0)
(0 0 1 0 1 0 0)
(0 0 1 0 1 1 1)
(0 0 1 0 1 0 1)
Good mutations
vertex 1 -> Algebra 245 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 167 permutation [ 2, 1, 5, 4, 3, 7, 6 ]
vertex 6 -> Algebra 165 permutation [ 2, 1, 5, 4, 3, 7, 6 ]
Algebra 302
Quiver
[ 2, 1 ], [ 2, 7 ], [ 3, 5 ], [ 3, 6 ], [ 4, 7 ], [ 6, 2 ], [ 6, 4 ], [ 7, 6 ]
Relations
[ 7, 6, 2 ]
[ 7, 6, 4 ]
[ 2, 7, 6 ]
[ 4, 7, 6 ]
[ 6, 2, 7 ] - [ 6, 4, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 0 0 1)
(1 1 1 1 1 1 1)
(0 0 0 1 0 0 1)
(0 0 0 0 1 0 0)
(1 1 0 1 0 1 1)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 246 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 304 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 5 -> Algebra 297 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 142 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 303
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 4, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 6, 3, 2 ]
[ 2, 6, 3 ]
[ 4, 6, 3 ]
[ 6, 3, 4 ]
[ 3, 2, 6 ] - [ 3, 4, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 0 1 0)
(1 1 1 1 1 1 0)
(0 0 0 1 0 1 0)
(0 0 0 0 1 0 0)
(0 0 1 0 1 1 0)
(0 0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 247 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 144 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 298 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 168 permutation [ 2, 1, 6, 4, 3, 5, 7 ]
vertex 7 -> Algebra 142 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 304
Quiver
[ 2, 1 ], [ 2, 7 ], [ 3, 2 ], [ 3, 4 ], [ 3, 6 ], [ 4, 7 ], [ 5, 6 ], [ 7, 3 ]
Relations
[ 7, 3, 2 ]
[ 2, 7, 3 ]
[ 4, 7, 3 ]
[ 7, 3, 4 ]
[ 3, 2, 7 ] - [ 3, 4, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 0 0 1)
(1 1 1 1 0 1 1)
(0 0 0 1 0 0 1)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 248 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 143 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 207 permutation [ 4, 2, 1, 7, 3, 6, 5 ]
vertex 6 -> Algebra 302 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
Algebra 321
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 7 ], [ 4, 3 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 0 0 0 1)
(1 1 1 1 0 0 1)
(1 1 1 0 1 1 0)
(1 1 1 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 266 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 166 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 323 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 162 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 322
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 6 ], [ 4, 3 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 0 0 1 0)
(1 1 1 1 0 1 0)
(1 1 1 0 1 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 2 -> Algebra 267 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 167 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 205 permutation [ 3, 1, 2, 4, 6, 5, 7 ]
vertex 7 -> Algebra 162 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 323
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 7 ], [ 4, 3 ], [ 5, 3 ], [ 5, 6 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 3, 7, 5 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 0 0 0 1)
(1 1 1 1 0 0 1)
(1 1 1 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 2 -> Algebra 268 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 168 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 163 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 321 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 326
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 5, 6 ], [ 6, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 1 0 0 0)
(0 0 0 1 0 0 0)
(1 1 1 1 1 1 0)
(1 1 1 1 0 1 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 2 -> Algebra 271 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 205 permutation [ 3, 1, 2, 4, 6, 5, 7 ]
vertex 6 -> Algebra 167 permutation [ 1, 2, 3, 4, 5, 6, 7 ]