Algebra 83

Quiver

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

Relations

[ 5, 3, 4, 2 ] 
[ 4, 2, 5, 3 ] 
[ 2, 5, 3, 4 ] 
[ 3, 4, 2, 5 ] 
[ 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 1 1 1 0 0 0)
(0 1 0 1 1 0 1)
(0 0 1 1 1 0 1)
(0 0 1 1 1 1 0)
(0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra  130    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  218    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 130

Quiver

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

Relations

[ 5, 3, 4, 2 ] 
[ 4, 2, 5, 3 ] 
[ 2, 5, 3, 4 ] 
[ 3, 4, 2, 5 ] 
[ 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)
(1 1 1 1 0 0 0)
(1 1 0 1 1 0 1)
(0 0 1 1 1 0 1)
(0 0 1 1 1 1 0)
(0 0 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra   83    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  277    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 176

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  208    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra  186    permutation [ 1, 2, 4, 3, 5, 6, 7 ]

Algebra 186

Quiver

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

Relations

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

Cartan matrix

(1 0 0 0 1 0 1)
(1 1 1 0 0 0 0)
(1 0 1 1 1 0 1)
(0 1 1 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  336    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  239    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  176    permutation [ 1, 2, 4, 3, 5, 6, 7 ]

Algebra 208

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  218    permutation [ 1, 4, 3, 2, 5, 6, 7 ]
vertex  3 -> Algebra  176    permutation [ 1, 3, 2, 4, 5, 6, 7 ]

Algebra 218

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  365    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra   83    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  239    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex  4 -> Algebra  208    permutation [ 1, 4, 3, 2, 5, 6, 7 ]

Algebra 239

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  186    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  218    permutation [ 1, 2, 4, 3, 5, 6, 7 ]

Algebra 277

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  365    permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  130    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  294    permutation [ 1, 2, 4, 3, 5, 6, 7 ]

Algebra 294

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  277    permutation [ 1, 2, 4, 3, 5, 6, 7 ]

Algebra 336

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  186    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 365

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  218    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  277    permutation [ 2, 1, 3, 4, 5, 6, 7 ]