E7_2.html

Algebra 3

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ]

Cartan matrix

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

Good mutations

vertex  3 -> Algebra   16    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra   17    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 4

Quiver

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

Relations

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

Cartan matrix

(1 1 1 1 1 1 1)
(0 1 1 1 1 1 1)
(0 1 1 0 0 0 0)
(0 0 1 1 0 0 0)
(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   10    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra   21    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 10

Quiver

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

Relations

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

Cartan matrix

(1 0 0 0 0 0 0)
(1 1 1 1 1 1 1)
(1 1 1 0 0 0 0)
(0 0 1 1 0 0 0)
(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    4    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra   41    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   45    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 16

Quiver

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

Relations

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

Cartan matrix

(1 0 1 1 1 1 1)
(1 1 1 0 0 0 0)
(1 0 1 0 0 0 0)
(0 0 1 1 0 0 0)
(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   21    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra    3    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   65    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 17

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ]

Cartan matrix

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

Good mutations

vertex  4 -> Algebra    3    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   69    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 20

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ]

Cartan matrix

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

Good mutations

vertex  3 -> Algebra   65    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra   69    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   75    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra    3    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 21

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra    4    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra   16    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  7 -> Algebra   80    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 25

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   45    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra   80    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   90    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra    4    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 41

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ]

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   10    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  124    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  125    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  127    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 45

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  127    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  137    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   10    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 65

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   80    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  183    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   16    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 69

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ]

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  125    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  7 -> Algebra   17    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 74

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ]

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  182    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  192    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  202    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   75    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 75

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ]

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  183    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  125    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  5 -> Algebra  124    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  6 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   74    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 80

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra   65    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  6 -> Algebra  215    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   21    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 89

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  136    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  214    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   90    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 90

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  137    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  215    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   89    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 124

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ]

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   41    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra   75    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  7 -> Algebra  202    permutation [ 1, 3, 2, 4, 5, 7, 6 ]

Algebra 125

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ]

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   75    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  5 -> Algebra   41    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   69    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  7 -> Algebra  192    permutation [ 1, 3, 2, 4, 5, 7, 6 ]

Algebra 127

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ]

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   45    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  202    permutation [ 1, 3, 2, 4, 5, 7, 6 ]
vertex  5 -> Algebra  192    permutation [ 1, 3, 2, 4, 5, 7, 6 ]
vertex  6 -> Algebra  275    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   41    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 136

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   89    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  274    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  137    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 137

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   90    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  275    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   45    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  136    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 182

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  214    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra   74    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  183    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 183

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  215    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra   75    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   65    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  182    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 192

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ]

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   74    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  127    permutation [ 1, 3, 2, 4, 5, 7, 6 ]
vertex  6 -> Algebra  125    permutation [ 1, 3, 2, 4, 5, 7, 6 ]

Algebra 198

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ]

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  274    permutation [ 1, 3, 2, 4, 7, 5, 6 ]
vertex  5 -> Algebra  201    permutation [ 1, 2, 3, 4, 6, 5, 7 ]

Algebra 201

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ]

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  275    permutation [ 1, 3, 2, 4, 7, 5, 6 ]
vertex  5 -> Algebra  202    permutation [ 1, 2, 3, 4, 7, 6, 5 ]
vertex  6 -> Algebra  198    permutation [ 1, 2, 3, 4, 6, 5, 7 ]

Algebra 202

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ]

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  127    permutation [ 1, 3, 2, 4, 5, 7, 6 ]
vertex  5 -> Algebra   74    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  124    permutation [ 1, 3, 2, 4, 5, 7, 6 ]
vertex  7 -> Algebra  201    permutation [ 1, 2, 3, 4, 7, 6, 5 ]

Algebra 214

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   89    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  182    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  6 -> Algebra  215    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 215

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   90    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  183    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  6 -> Algebra   80    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  214    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 274

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ]

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  136    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  198    permutation [ 1, 3, 2, 4, 6, 7, 5 ]
vertex  6 -> Algebra  275    permutation [ 1, 2, 3, 4, 5, 7, 6 ]

Algebra 275

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ]

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  137    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  201    permutation [ 1, 3, 2, 4, 6, 7, 5 ]
vertex  6 -> Algebra  127    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  274    permutation [ 1, 2, 3, 4, 5, 7, 6 ]