Algebra 93
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 5, 3, 2 ]
[ 2, 5, 3 ]
[ 4, 5, 3 ]
[ 5, 3, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 3, 2, 5 ] - [ 3, 4, 5 ]
Cartan matrix
(1 1 0 0 1 0 1)
(0 1 0 0 1 0 1)
(0 1 1 1 1 0 1)
(0 0 0 1 1 0 1)
(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 140 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 244 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 140
Quiver
[ 2, 1 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 5, 3, 2 ]
[ 2, 5, 3 ]
[ 4, 5, 3 ]
[ 5, 3, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 3, 2, 5 ] - [ 3, 4, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 1 0 1)
(1 1 1 1 1 0 1)
(0 0 0 1 1 0 1)
(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 93 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 299 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 244
Quiver
[ 1, 2 ], [ 2, 7 ], [ 3, 5 ], [ 4, 7 ], [ 5, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ]
Relations
[ 7, 5, 2 ]
[ 5, 6, 3 ]
[ 7, 5, 4 ]
[ 2, 7, 5 ]
[ 4, 7, 5 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 2, 7 ] - [ 5, 4, 7 ]
Cartan matrix
(1 1 0 0 0 0 1)
(0 1 0 0 0 0 1)
(0 1 1 1 1 0 1)
(0 0 0 1 0 0 1)
(0 1 0 1 1 1 1)
(0 0 1 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 299 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 93 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 299
Quiver
[ 2, 1 ], [ 2, 7 ], [ 3, 5 ], [ 4, 7 ], [ 5, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ]
Relations
[ 7, 5, 2 ]
[ 5, 6, 3 ]
[ 7, 5, 4 ]
[ 2, 7, 5 ]
[ 4, 7, 5 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 2, 7 ] - [ 5, 4, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 0 0 0 0 1)
(1 1 1 1 1 0 1)
(0 0 0 1 0 0 1)
(1 1 0 1 1 1 1)
(0 0 1 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 244 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 140 permutation [ 1, 2, 3, 4, 5, 6, 7 ]