Algebra 233

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  289    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  383    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  259    permutation [ 1, 2, 5, 4, 3, 6, 7 ]

Algebra 258

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  313    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  259    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 259

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  314    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  233    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  7 -> Algebra  258    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 289

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  233    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  314    permutation [ 1, 2, 5, 4, 3, 6, 7 ]

Algebra 313

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  258    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  381    permutation [ 6, 4, 1, 7, 2, 3, 5 ]
vertex  6 -> Algebra  314    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 314

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  259    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  289    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  7 -> Algebra  313    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 381

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  383    permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex  5 -> Algebra  313    permutation [ 3, 5, 6, 2, 7, 1, 4 ]

Algebra 383

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  233    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  381    permutation [ 1, 6, 3, 4, 5, 2, 7 ]