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 ]