Algebra 1
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 1 1 1 1 1)
(0 1 1 1 1 1 1)
(0 0 1 1 1 1 1)
(0 0 0 1 0 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 2 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 5 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 8 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 2
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 1 1 1)
(0 0 1 1 1 1 1)
(0 0 0 1 0 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 1 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 9 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 14 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 5
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 1 0 1 1 1)
(0 1 1 0 1 1 1)
(0 0 1 0 1 1 1)
(0 0 1 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)
Good mutations
vertex 1 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 1 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 29 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 8
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
Cartan matrix
(1 1 1 1 1 1 0)
(0 1 1 1 1 1 0)
(0 0 1 1 1 1 0)
(0 0 0 1 0 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 14 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 29 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 35 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 1 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 9
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 1 1 1 1)
(0 0 0 1 0 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 15 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 2 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 36 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 37 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 40 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 11
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 1 1)
(0 0 1 0 1 1 1)
(0 0 1 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)
Good mutations
vertex 1 -> Algebra 5 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 37 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 2 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 49 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 14
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 1 1 0)
(0 0 1 1 1 1 0)
(0 0 0 1 0 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 8 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 40 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 49 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 55 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 2 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 15
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 3, 5 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 1 1 1 1)
(0 0 0 1 0 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 9 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 56 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 57 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 60 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 29
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
Cartan matrix
(1 1 1 0 1 1 0)
(0 1 1 0 1 1 0)
(0 0 1 0 1 1 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 0 1 1)
Good mutations
vertex 1 -> Algebra 49 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 8 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 100 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 5 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 34
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 6, 7 ], [ 7, 5 ]
Relations
None
Cartan matrix
(1 1 1 1 1 0 0)
(0 1 1 1 1 0 0)
(0 0 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 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 54 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 99 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 110 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 35 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 35
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 6, 5 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 1 1 1 0 0)
(0 1 1 1 1 0 0)
(0 0 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 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 55 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 100 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 111 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 8 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 34 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 36
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 3 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
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 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 56 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 9 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 111 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 100 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 113 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 37
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 0 1 1 1)
(0 1 1 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)
Good mutations
vertex 1 -> Algebra 57 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 9 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 117 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 40
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 1 1 1 0)
(0 0 0 1 0 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 60 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 14 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 113 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 117 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 123 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 9 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 49
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 1 0)
(0 0 1 0 1 1 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 0 1 1)
Good mutations
vertex 1 -> Algebra 29 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 117 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 14 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 147 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 54
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 6, 7 ], [ 7, 5 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 1 0 0)
(0 0 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 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 34 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 122 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 146 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 157 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 55 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 55
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 6, 5 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 1 0 0)
(0 0 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 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 35 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 123 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 147 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 158 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 14 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 54 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 56
Quiver
[ 1, 2 ], [ 1, 3 ], [ 4, 3 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
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 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 61 permutation [ 3, 2, 1, 4, 5, 6, 7 ]
vertex 2 -> Algebra 36 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 15 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 158 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 147 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 160 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 57
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 0 1 1 1)
(1 1 1 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)
Good mutations
vertex 2 -> Algebra 37 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 15 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 164 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 60
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 3, 5 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 1 1 1 0)
(0 0 0 1 0 0 0)
(0 0 0 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 40 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 160 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 164 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 170 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 15 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 61
Quiver
[ 1, 3 ], [ 2, 3 ], [ 4, 1 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
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 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 76 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 56 permutation [ 3, 2, 1, 4, 5, 6, 7 ]
vertex 4 -> Algebra 171 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 172 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 174 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 76
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 1 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
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 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 61 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 203 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 204 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 206 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 99
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
None
Cartan matrix
(1 1 1 0 1 0 0)
(0 1 1 0 1 0 0)
(0 0 1 0 1 0 0)
(0 0 1 1 1 0 0)
(0 0 0 0 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 146 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 34 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 113 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
vertex 6 -> Algebra 100 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 100
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 1 0 1 0 0)
(0 1 1 0 1 0 0)
(0 0 1 0 1 0 0)
(0 0 1 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)
Good mutations
vertex 1 -> Algebra 147 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 35 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 36 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 29 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 99 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 106
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 5, 6 ], [ 6, 7 ], [ 7, 3 ]
Relations
None
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 1)
(0 0 1 1 0 1 1)
(0 0 1 1 0 0 1)
Good mutations
vertex 1 -> Algebra 153 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 249 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 109 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 109
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 5, 6 ], [ 5, 7 ], [ 7, 3 ]
Relations
None
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 1)
(0 0 0 0 0 1 0)
(0 0 1 1 0 0 1)
Good mutations
vertex 1 -> Algebra 156 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 250 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 110 permutation [ 1, 2, 3, 4, 7, 6, 5 ]
vertex 6 -> Algebra 106 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 110
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 5, 3 ], [ 5, 7 ], [ 6, 7 ]
Relations
None
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 0 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 157 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 113 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
vertex 5 -> Algebra 34 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 111 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
vertex 7 -> Algebra 109 permutation [ 1, 2, 3, 4, 7, 6, 5 ]
Algebra 111
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
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 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 158 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 36 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 35 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 110 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 113
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 3 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
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 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 160 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 40 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 110 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
vertex 5 -> Algebra 99 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
vertex 6 -> Algebra 250 permutation [ 1, 2, 3, 4, 6, 7, 5 ]
vertex 7 -> Algebra 36 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 117
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 0 1 1 0)
(0 1 1 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)
Good mutations
vertex 1 -> Algebra 164 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 49 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 40 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 172 permutation [ 3, 1, 2, 4, 5, 6, 7 ]
vertex 7 -> Algebra 37 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 122
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 6, 7 ], [ 7, 5 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 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 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 169 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 54 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 249 permutation [ 1, 2, 3, 4, 6, 7, 5 ]
vertex 4 -> Algebra 269 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 273 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 123 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 123
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], [ 6, 5 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 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 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 170 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 55 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 250 permutation [ 1, 2, 3, 4, 6, 7, 5 ]
vertex 4 -> Algebra 172 permutation [ 3, 1, 2, 4, 5, 6, 7 ]
vertex 5 -> Algebra 171 permutation [ 3, 1, 2, 4, 5, 6, 7 ]
vertex 6 -> Algebra 40 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 122 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 146
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 0 0)
(0 0 1 0 1 0 0)
(0 0 1 1 1 0 0)
(0 0 0 0 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 99 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 269 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 54 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 160 permutation [ 2, 1, 3, 4, 5, 7, 6 ]
vertex 6 -> Algebra 147 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 147
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 0 0)
(0 0 1 0 1 0 0)
(0 0 1 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)
Good mutations
vertex 1 -> Algebra 100 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 172 permutation [ 3, 1, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 55 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 56 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 49 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 146 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 153
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 5, 6 ], [ 6, 7 ], [ 7, 3 ]
Relations
None
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 1)
(0 0 1 1 0 1 1)
(0 0 1 1 0 0 1)
Good mutations
vertex 1 -> Algebra 106 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 270 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 305 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 156 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 156
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 5, 6 ], [ 5, 7 ], [ 7, 3 ]
Relations
None
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 1)
(0 0 0 0 0 1 0)
(0 0 1 1 0 0 1)
Good mutations
vertex 1 -> Algebra 109 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 272 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 306 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 157 permutation [ 1, 2, 3, 4, 7, 6, 5 ]
vertex 6 -> Algebra 153 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 157
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 5, 3 ], [ 5, 7 ], [ 6, 7 ]
Relations
None
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 0 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 110 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 273 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 160 permutation [ 2, 1, 3, 4, 5, 7, 6 ]
vertex 5 -> Algebra 54 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 158 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
vertex 7 -> Algebra 156 permutation [ 1, 2, 3, 4, 7, 6, 5 ]
Algebra 158
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
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 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 111 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 171 permutation [ 3, 1, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 56 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 55 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 157 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 160
Quiver
[ 1, 2 ], [ 1, 3 ], [ 4, 3 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
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 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 174 permutation [ 3, 2, 1, 4, 5, 6, 7 ]
vertex 2 -> Algebra 113 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 60 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 157 permutation [ 2, 1, 3, 4, 5, 7, 6 ]
vertex 5 -> Algebra 146 permutation [ 2, 1, 3, 4, 5, 7, 6 ]
vertex 6 -> Algebra 306 permutation [ 2, 1, 3, 4, 6, 7, 5 ]
vertex 7 -> Algebra 56 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 164
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 0 1 1 0)
(1 1 1 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)
Good mutations
vertex 2 -> Algebra 117 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 60 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 204 permutation [ 3, 1, 2, 4, 5, 6, 7 ]
vertex 7 -> Algebra 57 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 169
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 3, 5 ], [ 6, 7 ], [ 7, 5 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 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 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 2 -> Algebra 122 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 305 permutation [ 2, 1, 3, 4, 6, 7, 5 ]
vertex 4 -> Algebra 324 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 328 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 170 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 170
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 3, 5 ], [ 6, 5 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 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 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 123 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 306 permutation [ 2, 1, 3, 4, 6, 7, 5 ]
vertex 4 -> Algebra 204 permutation [ 3, 1, 2, 4, 5, 6, 7 ]
vertex 5 -> Algebra 203 permutation [ 3, 1, 2, 4, 5, 6, 7 ]
vertex 6 -> Algebra 60 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 169 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 171
Quiver
[ 1, 3 ], [ 1, 4 ], [ 2, 3 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 0 1 1 0 0 0)
(0 1 1 0 0 0 0)
(0 0 1 0 0 0 0)
(0 0 0 1 0 0 0)
(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 203 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 158 permutation [ 2, 3, 1, 4, 5, 6, 7 ]
vertex 4 -> Algebra 61 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 123 permutation [ 2, 3, 1, 4, 5, 6, 7 ]
vertex 7 -> Algebra 273 permutation [ 2, 3, 1, 4, 5, 7, 6 ]
Algebra 172
Quiver
[ 1, 3 ], [ 1, 5 ], [ 2, 3 ], [ 4, 1 ], [ 6, 5 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 0 1 0 1 0 0)
(0 1 1 0 0 0 0)
(0 0 1 0 0 0 0)
(1 0 1 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)
Good mutations
vertex 2 -> Algebra 204 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 147 permutation [ 2, 3, 1, 4, 5, 6, 7 ]
vertex 4 -> Algebra 123 permutation [ 2, 3, 1, 4, 5, 6, 7 ]
vertex 5 -> Algebra 61 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 117 permutation [ 2, 3, 1, 4, 5, 6, 7 ]
vertex 7 -> Algebra 269 permutation [ 2, 3, 1, 4, 5, 7, 6 ]
Algebra 174
Quiver
[ 1, 3 ], [ 2, 3 ], [ 4, 1 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
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 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 206 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 160 permutation [ 3, 2, 1, 4, 5, 6, 7 ]
vertex 4 -> Algebra 273 permutation [ 2, 3, 1, 4, 5, 7, 6 ]
vertex 5 -> Algebra 269 permutation [ 2, 3, 1, 4, 5, 7, 6 ]
vertex 6 -> Algebra 330 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 61 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 203
Quiver
[ 1, 2 ], [ 1, 4 ], [ 2, 3 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 1 1 0 0 0)
(0 1 1 0 0 0 0)
(0 0 1 0 0 0 0)
(0 0 0 1 0 0 0)
(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 171 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 76 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 170 permutation [ 2, 3, 1, 4, 5, 6, 7 ]
vertex 7 -> Algebra 328 permutation [ 2, 3, 1, 4, 5, 7, 6 ]
Algebra 204
Quiver
[ 1, 2 ], [ 1, 5 ], [ 2, 3 ], [ 4, 1 ], [ 6, 5 ], [ 6, 7 ]
Relations
None
Cartan matrix
(1 1 1 0 1 0 0)
(0 1 1 0 0 0 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 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 172 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 170 permutation [ 2, 3, 1, 4, 5, 6, 7 ]
vertex 5 -> Algebra 76 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 164 permutation [ 2, 3, 1, 4, 5, 6, 7 ]
vertex 7 -> Algebra 324 permutation [ 2, 3, 1, 4, 5, 7, 6 ]
Algebra 206
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 1 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ]
Relations
None
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 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 3 -> Algebra 174 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 328 permutation [ 2, 3, 1, 4, 5, 7, 6 ]
vertex 5 -> Algebra 324 permutation [ 2, 3, 1, 4, 5, 7, 6 ]
vertex 6 -> Algebra 357 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 76 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 249
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 3 ]
Relations
None
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 1 1)
(0 0 1 0 0 1 1)
(0 0 1 0 0 0 1)
Good mutations
vertex 1 -> Algebra 305 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 122 permutation [ 1, 2, 3, 4, 7, 5, 6 ]
vertex 4 -> Algebra 106 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 250 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 250
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 3 ], [ 5, 6 ], [ 5, 7 ], [ 7, 3 ]
Relations
None
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 1 1)
(0 0 0 0 0 1 0)
(0 0 1 0 0 0 1)
Good mutations
vertex 1 -> Algebra 306 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 123 permutation [ 1, 2, 3, 4, 7, 5, 6 ]
vertex 4 -> Algebra 109 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 113 permutation [ 1, 2, 3, 4, 7, 5, 6 ]
vertex 6 -> Algebra 249 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 269
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(0 1 1 0 1 0 0)
(0 1 1 1 1 0 0)
(0 0 0 0 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 1 -> Algebra 324 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 146 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 122 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 174 permutation [ 3, 1, 2, 4, 5, 7, 6 ]
vertex 6 -> Algebra 172 permutation [ 3, 1, 2, 4, 5, 7, 6 ]
Algebra 270
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 5, 6 ], [ 6, 7 ], [ 7, 3 ]
Relations
None
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 1)
(0 1 1 1 0 1 1)
(0 1 1 1 0 0 1)
Good mutations
vertex 1 -> Algebra 325 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 153 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 329 permutation [ 3, 1, 2, 4, 7, 5, 6 ]
vertex 5 -> Algebra 272 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 272
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 5, 6 ], [ 5, 7 ], [ 7, 3 ]
Relations
None
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 1)
(0 0 0 0 0 1 0)
(0 1 1 1 0 0 1)
Good mutations
vertex 1 -> Algebra 327 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 156 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 330 permutation [ 3, 1, 2, 4, 7, 5, 6 ]
vertex 5 -> Algebra 273 permutation [ 1, 2, 3, 4, 7, 6, 5 ]
vertex 6 -> Algebra 270 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 273
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 5, 3 ], [ 5, 7 ], [ 6, 7 ]
Relations
None
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 0 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 328 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 157 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 174 permutation [ 3, 1, 2, 4, 5, 7, 6 ]
vertex 5 -> Algebra 122 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 171 permutation [ 3, 1, 2, 4, 5, 7, 6 ]
vertex 7 -> Algebra 272 permutation [ 1, 2, 3, 4, 7, 6, 5 ]
Algebra 305
Quiver
[ 2, 1 ], [ 2, 3 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 3 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0 0)
(1 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 1 1)
(0 0 1 0 0 1 1)
(0 0 1 0 0 0 1)
Good mutations
vertex 1 -> Algebra 249 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 329 permutation [ 3, 1, 2, 4, 7, 5, 6 ]
vertex 3 -> Algebra 169 permutation [ 2, 1, 3, 4, 7, 5, 6 ]
vertex 4 -> Algebra 153 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 306 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 306
Quiver
[ 2, 1 ], [ 2, 3 ], [ 4, 3 ], [ 5, 6 ], [ 5, 7 ], [ 7, 3 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0 0)
(1 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 1 1)
(0 0 0 0 0 1 0)
(0 0 1 0 0 0 1)
Good mutations
vertex 1 -> Algebra 250 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 330 permutation [ 3, 1, 2, 4, 7, 5, 6 ]
vertex 3 -> Algebra 170 permutation [ 2, 1, 3, 4, 7, 5, 6 ]
vertex 4 -> Algebra 156 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 160 permutation [ 2, 1, 3, 4, 7, 5, 6 ]
vertex 6 -> Algebra 305 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 324
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 0 0)
(1 1 1 0 1 0 0)
(1 1 1 1 1 0 0)
(0 0 0 0 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 1 0 1)
Good mutations
vertex 2 -> Algebra 269 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 169 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 206 permutation [ 3, 1, 2, 4, 5, 7, 6 ]
vertex 6 -> Algebra 204 permutation [ 3, 1, 2, 4, 5, 7, 6 ]
Algebra 325
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 5, 6 ], [ 6, 7 ], [ 7, 3 ]
Relations
None
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 1)
(1 1 1 1 0 1 1)
(1 1 1 1 0 0 1)
Good mutations
vertex 2 -> Algebra 270 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 356 permutation [ 3, 1, 2, 4, 7, 5, 6 ]
vertex 5 -> Algebra 327 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 327
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 5, 6 ], [ 5, 7 ], [ 7, 3 ]
Relations
None
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 1)
(0 0 0 0 0 1 0)
(1 1 1 1 0 0 1)
Good mutations
vertex 2 -> Algebra 272 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 357 permutation [ 3, 1, 2, 4, 7, 5, 6 ]
vertex 5 -> Algebra 328 permutation [ 1, 2, 3, 4, 7, 6, 5 ]
vertex 6 -> Algebra 325 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 328
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 5, 3 ], [ 5, 7 ], [ 6, 7 ]
Relations
None
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 0 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 273 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 206 permutation [ 3, 1, 2, 4, 5, 7, 6 ]
vertex 5 -> Algebra 169 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 203 permutation [ 3, 1, 2, 4, 5, 7, 6 ]
vertex 7 -> Algebra 327 permutation [ 1, 2, 3, 4, 7, 6, 5 ]
Algebra 329
Quiver
[ 1, 3 ], [ 2, 3 ], [ 4, 1 ], [ 5, 1 ], [ 6, 7 ], [ 7, 5 ]
Relations
None
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 0)
(1 0 1 0 1 1 1)
(1 0 1 0 1 0 1)
Good mutations
vertex 2 -> Algebra 356 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 305 permutation [ 2, 3, 1, 4, 6, 7, 5 ]
vertex 4 -> Algebra 270 permutation [ 2, 3, 1, 4, 6, 7, 5 ]
vertex 6 -> Algebra 330 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 330
Quiver
[ 1, 3 ], [ 2, 3 ], [ 4, 1 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ]
Relations
None
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 0)
(1 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 357 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 306 permutation [ 2, 3, 1, 4, 6, 7, 5 ]
vertex 4 -> Algebra 272 permutation [ 2, 3, 1, 4, 6, 7, 5 ]
vertex 6 -> Algebra 174 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 329 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 356
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 1 ], [ 5, 1 ], [ 6, 7 ], [ 7, 5 ]
Relations
None
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 0)
(1 1 1 0 1 1 1)
(1 1 1 0 1 0 1)
Good mutations
vertex 3 -> Algebra 329 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 325 permutation [ 2, 3, 1, 4, 6, 7, 5 ]
vertex 6 -> Algebra 357 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 357
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 1 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ]
Relations
None
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 0)
(1 1 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 330 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 327 permutation [ 2, 3, 1, 4, 6, 7, 5 ]
vertex 6 -> Algebra 206 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 356 permutation [ 1, 2, 3, 4, 5, 7, 6 ]