Algebra 114

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]

Relations

[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 2, 3 ] - [ 4, 5, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0)
(0 1 1 0 0 0 0)
(0 0 1 1 0 0 0)
(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  161    permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  264    permutation [ 1, 2, 4, 3, 5, 7, 6 ]

Algebra 161

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ]

Relations

[ 3, 4, 1 ] 
[ 1, 3, 4 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 4, 1, 3 ] - [ 4, 5, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0)
(0 1 0 0 0 0 0)
(0 0 1 1 0 0 0)
(1 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  2 -> Algebra  114    permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  319    permutation [ 2, 1, 4, 3, 5, 7, 6 ]

Algebra 178

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 5 ], [ 4, 1 ], [ 4, 3 ], [ 5, 4 ], [ 6, 1 ], [ 6, 7 ]

Relations

[ 5, 4, 1 ] 
[ 5, 4, 3 ] 
[ 1, 5, 4 ] 
[ 3, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 3, 5 ] 

Cartan matrix

(1 0 0 0 1 0 0)
(0 1 1 0 1 0 0)
(0 0 1 0 1 0 0)
(1 0 1 1 1 0 0)
(0 0 0 1 1 0 0)
(1 0 0 0 1 1 1)
(0 0 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  210    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  6 -> Algebra  264    permutation [ 2, 3, 4, 5, 1, 7, 6 ]
vertex  7 -> Algebra  261    permutation [ 2, 3, 4, 5, 7, 6, 1 ]

Algebra 210

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 5 ], [ 4, 1 ], [ 4, 2 ], [ 5, 4 ], [ 6, 1 ], [ 6, 7 ]

Relations

[ 5, 4, 1 ] 
[ 5, 4, 2 ] 
[ 1, 5, 4 ] 
[ 2, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 2, 5 ] 

Cartan matrix

(1 0 0 0 1 0 0)
(0 1 1 0 1 0 0)
(0 0 1 0 0 0 0)
(1 1 1 1 1 0 0)
(0 0 0 1 1 0 0)
(1 0 0 0 1 1 1)
(0 0 0 0 0 0 1)

Good mutations

vertex  3 -> Algebra  178    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  6 -> Algebra  319    permutation [ 3, 2, 4, 5, 1, 7, 6 ]
vertex  7 -> Algebra  316    permutation [ 3, 2, 4, 5, 7, 6, 1 ]

Algebra 261

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 2 ], [ 3, 7 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ]

Relations

[ 4, 3, 2 ] 
[ 2, 4, 3 ] 
[ 7, 4, 3 ] 
[ 4, 3, 7 ] 
[ 3, 2, 4 ] - [ 3, 7, 4 ] 

Cartan matrix

(1 1 0 1 0 0 0)
(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 1)
(0 0 0 1 0 1 1)
(0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  316    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  178    permutation [ 7, 1, 2, 3, 4, 6, 5 ]

Algebra 264

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ]

Relations

[ 4, 3, 2 ] 
[ 2, 4, 3 ] 
[ 5, 4, 3 ] 
[ 4, 3, 5 ] 
[ 3, 2, 4 ] - [ 3, 5, 4 ] 

Cartan matrix

(1 1 0 1 0 0 0)
(0 1 0 1 0 0 0)
(0 1 1 1 1 0 1)
(0 0 1 1 0 0 0)
(0 0 0 1 1 0 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  319    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  114    permutation [ 1, 2, 4, 3, 5, 7, 6 ]
vertex  7 -> Algebra  178    permutation [ 5, 1, 2, 3, 4, 7, 6 ]

Algebra 316

Quiver

[ 2, 1 ], [ 2, 4 ], [ 3, 2 ], [ 3, 7 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ]

Relations

[ 4, 3, 2 ] 
[ 2, 4, 3 ] 
[ 7, 4, 3 ] 
[ 4, 3, 7 ] 
[ 3, 2, 4 ] - [ 3, 7, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0)
(1 1 0 1 0 0 0)
(1 1 1 1 0 0 1)
(0 0 1 1 0 0 0)
(0 0 0 1 1 1 1)
(0 0 0 1 0 1 1)
(0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  261    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  210    permutation [ 7, 2, 1, 3, 4, 6, 5 ]

Algebra 319

Quiver

[ 2, 1 ], [ 2, 4 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ]

Relations

[ 4, 3, 2 ] 
[ 2, 4, 3 ] 
[ 5, 4, 3 ] 
[ 4, 3, 5 ] 
[ 3, 2, 4 ] - [ 3, 5, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0)
(1 1 0 1 0 0 0)
(1 1 1 1 1 0 1)
(0 0 1 1 0 0 0)
(0 0 0 1 1 0 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  264    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  161    permutation [ 2, 1, 4, 3, 5, 7, 6 ]
vertex  7 -> Algebra  210    permutation [ 5, 2, 1, 3, 4, 7, 6 ]