Algebra 70
Quiver
[ 1, 4 ], [ 1, 6 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 4, 3, 1 ]
[ 6, 3, 1 ]
[ 3, 5, 2 ]
[ 2, 3, 5 ]
[ 4, 3, 5 ]
[ 3, 1, 6 ]
[ 1, 4, 3 ] - [ 1, 6, 3 ]
[ 5, 2, 3 ] - [ 5, 4, 3 ]
[ 3, 1, 4 ] - [ 3, 5, 4 ]
Cartan matrix
(1 0 1 1 0 1 1)
(1 1 1 0 0 0 0)
(1 0 1 1 1 0 0)
(0 0 1 1 0 0 0)
(0 1 1 1 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 101 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 194 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 195 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 196 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 86
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 7 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 4, 3, 5, 6, 2 ]
[ 7, 6, 2 ]
[ 5, 6, 2, 4, 3 ]
[ 3, 5, 6, 2, 4 ]
[ 6, 2, 4, 3, 5 ]
[ 6, 2, 7 ]
[ 2, 4, 3, 5, 6 ] - [ 2, 7, 6 ]
Cartan matrix
(1 1 1 1 1 1 1)
(0 1 1 1 1 1 1)
(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 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 133 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 231 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 222 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 88 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 88
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 7 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ]
Relations
[ 4, 3, 5, 2 ]
[ 7, 5, 2 ]
[ 3, 5, 2, 4 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 2, 7 ]
[ 5, 2, 4, 3 ] - [ 5, 6, 3 ]
[ 2, 4, 3, 5 ] - [ 2, 7, 5 ]
Cartan matrix
(1 1 1 1 1 0 1)
(0 1 1 1 1 0 1)
(0 1 1 0 1 0 0)
(0 0 1 1 1 0 0)
(0 1 1 1 1 1 0)
(0 0 1 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 135 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 234 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 86 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 179 permutation [ 5, 1, 2, 7, 4, 3, 6 ]
Algebra 101
Quiver
[ 1, 4 ], [ 1, 6 ], [ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 2 ], [ 5, 4 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 4, 2, 1 ]
[ 6, 2, 1 ]
[ 3, 5, 4, 2 ]
[ 5, 4, 2, 3 ]
[ 4, 2, 3, 5 ]
[ 2, 1, 6 ]
[ 1, 4, 2 ] - [ 1, 6, 2 ]
[ 2, 1, 4 ] - [ 2, 3, 5, 4 ]
Cartan matrix
(1 1 1 1 0 1 1)
(1 1 1 1 1 0 0)
(0 0 1 1 1 0 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 0 0)
(0 1 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 251 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 70 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 252 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 253 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 254 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 133
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 7 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 4, 3, 5, 6, 2 ]
[ 7, 6, 2 ]
[ 5, 6, 2, 4, 3 ]
[ 3, 5, 6, 2, 4 ]
[ 6, 2, 4, 3, 5 ]
[ 6, 2, 7 ]
[ 2, 4, 3, 5, 6 ] - [ 2, 7, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 1 1 1)
(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 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 86 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 287 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 280 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 135 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 135
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 7 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ]
Relations
[ 4, 3, 5, 2 ]
[ 7, 5, 2 ]
[ 3, 5, 2, 4 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 2, 7 ]
[ 5, 2, 4, 3 ] - [ 5, 6, 3 ]
[ 2, 4, 3, 5 ] - [ 2, 7, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 1 0 1)
(1 1 1 0 1 0 0)
(0 0 1 1 1 0 0)
(1 1 1 1 1 1 0)
(0 0 1 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 88 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 290 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 133 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 211 permutation [ 5, 2, 1, 7, 4, 3, 6 ]
Algebra 179
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 6, 1 ], [ 7, 6 ]
Relations
[ 4, 3, 5, 6, 1 ]
[ 7, 6, 1 ]
[ 5, 6, 1, 4, 3 ]
[ 3, 5, 6, 1, 4 ]
[ 6, 1, 4, 3, 5 ]
[ 6, 1, 7 ]
[ 1, 4, 3, 5, 6 ] - [ 1, 7, 6 ]
Cartan matrix
(1 0 1 1 1 1 1)
(1 1 1 0 1 1 0)
(1 0 1 0 1 1 0)
(0 0 1 1 1 1 0)
(1 0 0 1 1 1 0)
(1 0 1 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 211 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 195 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 88 permutation [ 2, 3, 6, 5, 1, 7, 4 ]
vertex 5 -> Algebra 181 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 181
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 1 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ]
Relations
[ 4, 3, 5, 1 ]
[ 7, 5, 1 ]
[ 3, 5, 1, 4 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 1, 7 ]
[ 5, 1, 4, 3 ] - [ 5, 6, 3 ]
[ 1, 4, 3, 5 ] - [ 1, 7, 5 ]
Cartan matrix
(1 0 1 1 1 0 1)
(1 1 1 0 1 0 0)
(1 0 1 0 1 0 0)
(0 0 1 1 1 0 0)
(1 0 1 1 1 1 0)
(0 0 1 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 2 -> Algebra 213 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 200 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 179 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 333 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 185
Quiver
[ 1, 6 ], [ 2, 3 ], [ 3, 5 ], [ 4, 2 ], [ 4, 6 ], [ 5, 1 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 6, 5, 1 ]
[ 3, 5, 4, 2 ]
[ 5, 4, 2, 3 ]
[ 2, 3, 5, 4 ]
[ 6, 5, 4 ]
[ 1, 6, 5 ]
[ 4, 2, 3, 5 ] - [ 4, 6, 5 ]
[ 5, 1, 6 ] - [ 5, 4, 6 ]
Cartan matrix
(1 0 0 0 0 1 1)
(1 1 1 0 1 0 0)
(1 0 1 1 1 1 1)
(0 1 1 1 1 1 1)
(1 1 0 1 1 1 1)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 338 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 188 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 263 permutation [ 2, 5, 1, 4, 6, 7, 3 ]
vertex 7 -> Algebra 287 permutation [ 1, 6, 2, 4, 3, 5, 7 ]
Algebra 188
Quiver
[ 1, 6 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 6 ], [ 5, 2 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 6, 3, 1 ]
[ 1, 6, 3 ]
[ 5, 2, 3 ]
[ 2, 3, 4 ]
[ 6, 3, 4 ]
[ 2, 3, 5 ]
[ 3, 4, 2 ] - [ 3, 5, 2 ]
[ 4, 2, 3 ] - [ 4, 6, 3 ]
[ 3, 1, 6 ] - [ 3, 4, 6 ]
Cartan matrix
(1 0 0 0 0 1 1)
(1 1 1 0 0 0 0)
(1 1 1 1 1 1 1)
(0 1 1 1 0 1 1)
(0 1 0 0 1 0 0)
(0 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 341 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 194 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 185 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 229 permutation [ 3, 4, 1, 6, 7, 2, 5 ]
vertex 7 -> Algebra 290 permutation [ 1, 6, 2, 4, 3, 5, 7 ]
Algebra 194
Quiver
[ 1, 6 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 6, 3, 4, 1 ]
[ 3, 4, 5, 2 ]
[ 1, 6, 3, 4 ]
[ 5, 2, 3, 4 ]
[ 2, 3, 4, 5 ]
[ 3, 4, 1, 6 ]
[ 4, 1, 6, 3 ] - [ 4, 5, 2, 3 ]
Cartan matrix
(1 0 1 0 0 1 1)
(1 1 1 1 0 0 0)
(1 0 1 1 1 0 0)
(1 1 1 1 1 1 1)
(0 1 1 0 1 0 0)
(0 0 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 345 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 252 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 188 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 4 -> Algebra 70 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 263 permutation [ 2, 4, 1, 3, 6, 7, 5 ]
vertex 6 -> Algebra 346 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 347 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 195
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 3 ], [ 3, 5 ], [ 3, 6 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 6, 1 ], [ 7, 6 ]
Relations
[ 4, 3, 6, 1 ]
[ 7, 6, 1 ]
[ 3, 5, 2 ]
[ 6, 1, 4, 3 ]
[ 2, 3, 5 ]
[ 4, 3, 5 ]
[ 6, 1, 7 ]
[ 5, 2, 3 ] - [ 5, 4, 3 ]
[ 3, 5, 4 ] - [ 3, 6, 1, 4 ]
[ 1, 4, 3, 6 ] - [ 1, 7, 6 ]
Cartan matrix
(1 0 1 1 0 1 1)
(1 1 1 0 0 1 0)
(1 0 1 1 1 1 0)
(0 0 1 1 0 1 0)
(0 1 1 1 1 1 0)
(1 0 0 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 253 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 197 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 4 -> Algebra 346 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 179 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 70 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 196
Quiver
[ 1, 4 ], [ 1, 6 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 4, 3, 1 ]
[ 6, 3, 1 ]
[ 3, 5, 2 ]
[ 2, 3, 5 ]
[ 4, 3, 5 ]
[ 3, 1, 6 ]
[ 1, 4, 3 ] - [ 1, 6, 3 ]
[ 5, 2, 3 ] - [ 5, 4, 3 ]
[ 3, 1, 4 ] - [ 3, 5, 4 ]
Cartan matrix
(1 0 1 1 0 1 0)
(1 1 1 0 0 0 0)
(1 0 1 1 1 0 0)
(0 0 1 1 0 0 0)
(0 1 1 1 1 0 0)
(0 0 1 0 1 1 0)
(0 0 1 0 1 1 1)
Good mutations
vertex 2 -> Algebra 254 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 347 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 70 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 197
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 3 ], [ 3, 1 ], [ 3, 6 ], [ 4, 3 ], [ 5, 6 ], [ 6, 2 ], [ 6, 4 ], [ 7, 3 ]
Relations
[ 4, 3, 1 ]
[ 7, 3, 1 ]
[ 3, 6, 2 ]
[ 2, 3, 6 ]
[ 4, 3, 6 ]
[ 3, 1, 7 ]
[ 1, 4, 3 ] - [ 1, 7, 3 ]
[ 6, 2, 3 ] - [ 6, 4, 3 ]
[ 3, 1, 4 ] - [ 3, 6, 4 ]
Cartan matrix
(1 0 1 1 0 0 1)
(1 1 1 0 0 0 0)
(1 0 1 1 0 1 0)
(0 0 1 1 0 0 0)
(0 1 1 1 1 1 0)
(0 1 1 1 0 1 0)
(0 0 1 0 0 1 1)
Good mutations
vertex 2 -> Algebra 260 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 352 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 200 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 195 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 7 -> Algebra 353 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 200
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 5, 6 ], [ 7, 3 ]
Relations
[ 4, 3, 1 ]
[ 7, 3, 1 ]
[ 3, 5, 2 ]
[ 2, 3, 5 ]
[ 4, 3, 5 ]
[ 3, 1, 7 ]
[ 1, 4, 3 ] - [ 1, 7, 3 ]
[ 5, 2, 3 ] - [ 5, 4, 3 ]
[ 3, 1, 4 ] - [ 3, 5, 4 ]
Cartan matrix
(1 0 1 1 0 0 1)
(1 1 1 0 0 0 0)
(1 0 1 1 1 1 0)
(0 0 1 1 0 0 0)
(0 1 1 1 1 1 0)
(0 0 0 0 0 1 0)
(0 0 1 0 1 1 1)
Good mutations
vertex 2 -> Algebra 263 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 338 permutation [ 2, 1, 7, 4, 3, 5, 6 ]
vertex 5 -> Algebra 181 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 197 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 345 permutation [ 2, 1, 4, 3, 7, 5, 6 ]
Algebra 211
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 3 ], [ 2, 5 ], [ 4, 2 ], [ 5, 6 ], [ 6, 1 ], [ 7, 6 ]
Relations
[ 4, 2, 5, 6, 1 ]
[ 7, 6, 1 ]
[ 5, 6, 1, 4, 2 ]
[ 2, 5, 6, 1, 4 ]
[ 6, 1, 4, 2, 5 ]
[ 6, 1, 7 ]
[ 1, 4, 2, 5, 6 ] - [ 1, 7, 6 ]
Cartan matrix
(1 1 1 1 1 1 1)
(1 1 1 0 1 1 0)
(0 0 1 0 0 0 0)
(0 1 1 1 1 1 0)
(1 0 0 1 1 1 0)
(1 1 1 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 229 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 3 -> Algebra 179 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 135 permutation [ 3, 2, 6, 5, 1, 7, 4 ]
vertex 5 -> Algebra 213 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 213
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 3 ], [ 2, 5 ], [ 4, 2 ], [ 5, 1 ], [ 5, 6 ], [ 6, 2 ], [ 7, 5 ]
Relations
[ 4, 2, 5, 1 ]
[ 7, 5, 1 ]
[ 2, 5, 1, 4 ]
[ 6, 2, 5 ]
[ 2, 5, 6 ]
[ 5, 1, 7 ]
[ 5, 1, 4, 2 ] - [ 5, 6, 2 ]
[ 1, 4, 2, 5 ] - [ 1, 7, 5 ]
Cartan matrix
(1 1 1 1 1 0 1)
(1 1 1 0 1 0 0)
(0 0 1 0 0 0 0)
(0 1 1 1 1 0 0)
(1 1 1 1 1 1 0)
(0 1 1 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 2 -> Algebra 234 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 3 -> Algebra 181 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 6 -> Algebra 211 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 361 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 222
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 7, 6, 2 ]
[ 4, 2, 3 ]
[ 5, 6, 2, 3 ]
[ 2, 3, 4 ]
[ 6, 2, 3, 5 ]
[ 6, 2, 7 ]
[ 3, 4, 2 ] - [ 3, 5, 6, 2 ]
[ 2, 3, 5, 6 ] - [ 2, 7, 6 ]
Cartan matrix
(1 1 1 0 1 1 1)
(0 1 1 0 1 1 1)
(0 1 1 1 1 1 0)
(0 1 0 1 0 0 1)
(0 1 0 0 1 1 0)
(0 1 1 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 280 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 376 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 86 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 333 permutation [ 6, 1, 2, 7, 3, 4, 5 ]
Algebra 229
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 5 ], [ 2, 6 ], [ 3, 5 ], [ 4, 2 ], [ 4, 3 ], [ 5, 4 ], [ 6, 1 ], [ 7, 6 ]
Relations
[ 4, 2, 6, 1 ]
[ 7, 6, 1 ]
[ 5, 4, 2 ]
[ 6, 1, 4, 2 ]
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 6, 1, 7 ]
[ 2, 5, 4 ] - [ 2, 6, 1, 4 ]
[ 4, 2, 5 ] - [ 4, 3, 5 ]
[ 1, 4, 2, 6 ] - [ 1, 7, 6 ]
Cartan matrix
(1 1 1 1 1 1 1)
(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 0 1 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 342 permutation [ 3, 6, 4, 2, 7, 1, 5 ]
vertex 2 -> Algebra 231 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex 3 -> Algebra 253 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 188 permutation [ 3, 6, 1, 2, 7, 4, 5 ]
vertex 5 -> Algebra 211 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
Algebra 231
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 1 ], [ 2, 6 ], [ 3, 5 ], [ 4, 2 ], [ 4, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 2 ]
Relations
[ 4, 2, 1 ]
[ 7, 2, 1 ]
[ 6, 4, 2 ]
[ 5, 6, 4, 3 ]
[ 3, 5, 6, 4 ]
[ 6, 4, 3, 5 ]
[ 2, 1, 7 ]
[ 1, 4, 2 ] - [ 1, 7, 2 ]
[ 2, 1, 4 ] - [ 2, 6, 4 ]
[ 4, 2, 6 ] - [ 4, 3, 5, 6 ]
Cartan matrix
(1 1 1 1 1 1 1)
(1 1 1 1 0 1 0)
(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 0 1 0)
(0 1 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 352 permutation [ 3, 2, 6, 4, 7, 1, 5 ]
vertex 2 -> Algebra 86 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 257 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 346 permutation [ 3, 2, 4, 1, 7, 6, 5 ]
vertex 5 -> Algebra 234 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 229 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
Algebra 234
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 1 ], [ 2, 5 ], [ 3, 5 ], [ 4, 2 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ]
Relations
[ 4, 2, 1 ]
[ 7, 2, 1 ]
[ 5, 4, 2 ]
[ 3, 5, 4 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 2, 1, 7 ]
[ 1, 4, 2 ] - [ 1, 7, 2 ]
[ 5, 4, 3 ] - [ 5, 6, 3 ]
[ 2, 1, 4 ] - [ 2, 5, 4 ]
[ 4, 2, 5 ] - [ 4, 3, 5 ]
Cartan matrix
(1 1 1 1 1 0 1)
(1 1 1 1 1 1 0)
(0 0 1 0 1 0 0)
(0 1 1 1 1 0 0)
(0 0 1 1 1 1 0)
(0 0 1 0 0 1 0)
(0 1 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 384 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 88 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 263 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 5 -> Algebra 213 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 6 -> Algebra 231 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 346 permutation [ 5, 1, 4, 2, 7, 3, 6 ]
Algebra 237
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 2, 3, 4, 5, 1 ]
[ 3, 4, 5, 1, 2 ]
[ 4, 5, 1, 2, 3 ]
[ 5, 1, 2, 3, 4 ]
[ 1, 2, 3, 4, 5 ]
Cartan matrix
(1 1 1 1 0 0 0)
(0 1 1 1 1 1 1)
(1 0 1 1 1 1 1)
(1 1 0 1 1 1 1)
(1 1 1 0 1 1 1)
(0 0 0 0 0 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 5 -> Algebra 385 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 387 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 251
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 1 ], [ 5, 4 ], [ 6, 1 ], [ 6, 7 ]
Relations
[ 2, 3, 5, 4, 1 ]
[ 3, 5, 4, 1, 2 ]
[ 5, 4, 1, 2, 3 ]
[ 1, 2, 3, 5, 4 ]
[ 4, 1, 2, 3, 5 ]
Cartan matrix
(1 1 1 0 1 0 0)
(0 1 1 1 1 0 0)
(1 0 1 1 1 0 0)
(1 1 1 1 0 0 0)
(1 1 0 1 1 0 0)
(1 1 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 101 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 6 -> Algebra 387 permutation [ 2, 3, 5, 4, 1, 6, 7 ]
vertex 7 -> Algebra 392 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 252
Quiver
[ 1, 6 ], [ 2, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 6, 2, 4, 1 ]
[ 3, 5, 2 ]
[ 5, 2, 3 ]
[ 1, 6, 2, 4 ]
[ 5, 2, 4 ]
[ 2, 4, 1, 6 ]
[ 4, 1, 6, 2 ] - [ 4, 5, 2 ]
[ 2, 3, 5 ] - [ 2, 4, 5 ]
Cartan matrix
(1 1 1 0 0 1 1)
(1 1 1 1 1 0 0)
(0 0 1 0 1 0 0)
(1 1 0 1 1 1 1)
(0 1 0 0 1 0 0)
(0 1 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 194 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 101 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 380 permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex 6 -> Algebra 376 permutation [ 4, 2, 1, 3, 7, 6, 5 ]
vertex 7 -> Algebra 368 permutation [ 4, 7, 1, 3, 6, 2, 5 ]
Algebra 253
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 4, 2 ], [ 5, 4 ], [ 6, 1 ], [ 7, 6 ]
Relations
[ 4, 2, 6, 1 ]
[ 7, 6, 1 ]
[ 3, 5, 4, 2 ]
[ 6, 1, 4, 2 ]
[ 5, 4, 2, 3 ]
[ 4, 2, 3, 5 ]
[ 6, 1, 7 ]
[ 2, 3, 5, 4 ] - [ 2, 6, 1, 4 ]
[ 1, 4, 2, 6 ] - [ 1, 7, 6 ]
Cartan matrix
(1 1 1 1 0 1 1)
(1 1 1 1 1 1 0)
(0 0 1 1 1 0 0)
(0 1 1 1 0 1 0)
(0 1 0 1 1 1 0)
(1 0 0 1 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 394 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 257 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex 3 -> Algebra 195 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 376 permutation [ 4, 2, 1, 3, 7, 6, 5 ]
vertex 5 -> Algebra 229 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 101 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 254
Quiver
[ 1, 4 ], [ 1, 6 ], [ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 2 ], [ 5, 4 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 4, 2, 1 ]
[ 6, 2, 1 ]
[ 3, 5, 4, 2 ]
[ 5, 4, 2, 3 ]
[ 4, 2, 3, 5 ]
[ 2, 1, 6 ]
[ 1, 4, 2 ] - [ 1, 6, 2 ]
[ 2, 1, 4 ] - [ 2, 3, 5, 4 ]
Cartan matrix
(1 1 1 1 0 1 0)
(1 1 1 1 1 0 0)
(0 0 1 1 1 0 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 0 0)
(0 1 1 0 1 1 0)
(0 1 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 392 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 196 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 368 permutation [ 4, 7, 1, 3, 6, 2, 5 ]
vertex 7 -> Algebra 101 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 257
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 1 ], [ 2, 6 ], [ 3, 5 ], [ 3, 6 ], [ 4, 2 ], [ 4, 3 ], [ 5, 4 ], [ 6, 4 ], [ 7, 2 ]
Relations
[ 4, 2, 1 ]
[ 7, 2, 1 ]
[ 6, 4, 2 ]
[ 5, 4, 3 ]
[ 6, 4, 3 ]
[ 4, 3, 5 ]
[ 2, 1, 7 ]
[ 1, 4, 2 ] - [ 1, 7, 2 ]
[ 2, 1, 4 ] - [ 2, 6, 4 ]
[ 3, 5, 4 ] - [ 3, 6, 4 ]
[ 4, 2, 6 ] - [ 4, 3, 6 ]
Cartan matrix
(1 1 1 1 0 1 1)
(1 1 0 1 0 1 0)
(0 0 1 1 1 1 0)
(0 1 1 1 0 1 0)
(0 1 0 1 1 0 0)
(0 0 0 1 0 1 0)
(0 1 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 397 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 260 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 4 -> Algebra 280 permutation [ 6, 4, 1, 3, 7, 2, 5 ]
vertex 5 -> Algebra 231 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 253 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
Algebra 260
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 1 ], [ 2, 3 ], [ 3, 6 ], [ 4, 2 ], [ 5, 6 ], [ 6, 4 ], [ 7, 2 ]
Relations
[ 4, 2, 1 ]
[ 7, 2, 1 ]
[ 3, 6, 4, 2 ]
[ 6, 4, 2, 3 ]
[ 4, 2, 3, 6 ]
[ 2, 1, 7 ]
[ 1, 4, 2 ] - [ 1, 7, 2 ]
[ 2, 1, 4 ] - [ 2, 3, 6, 4 ]
Cartan matrix
(1 1 1 1 0 0 1)
(1 1 1 1 0 1 0)
(0 0 1 1 0 1 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 1 0)
(0 1 0 1 0 1 0)
(0 1 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 400 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 197 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 287 permutation [ 3, 6, 1, 4, 7, 2, 5 ]
vertex 5 -> Algebra 263 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 257 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 7 -> Algebra 347 permutation [ 3, 1, 4, 2, 7, 6, 5 ]
Algebra 263
Quiver
[ 1, 4 ], [ 1, 7 ], [ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 7, 2 ]
Relations
[ 4, 2, 1 ]
[ 7, 2, 1 ]
[ 3, 5, 4, 2 ]
[ 5, 4, 2, 3 ]
[ 4, 2, 3, 5 ]
[ 2, 1, 7 ]
[ 1, 4, 2 ] - [ 1, 7, 2 ]
[ 2, 1, 4 ] - [ 2, 3, 5, 4 ]
Cartan matrix
(1 1 1 1 0 0 1)
(1 1 1 1 1 1 0)
(0 0 1 1 1 1 0)
(0 1 1 1 0 0 0)
(0 1 0 1 1 1 0)
(0 0 0 0 0 1 0)
(0 1 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 401 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 200 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 185 permutation [ 3, 1, 7, 4, 2, 5, 6 ]
vertex 5 -> Algebra 234 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 260 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 194 permutation [ 3, 1, 4, 2, 7, 5, 6 ]
Algebra 280
Quiver
[ 2, 1 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ]
Relations
[ 7, 6, 2 ]
[ 4, 2, 3 ]
[ 5, 6, 2, 3 ]
[ 2, 3, 4 ]
[ 6, 2, 3, 5 ]
[ 6, 2, 7 ]
[ 3, 4, 2 ] - [ 3, 5, 6, 2 ]
[ 2, 3, 5, 6 ] - [ 2, 7, 6 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 1 1)
(1 1 1 1 1 1 0)
(1 1 0 1 0 0 1)
(1 1 0 0 1 1 0)
(1 1 1 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 222 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 257 permutation [ 3, 6, 4, 2, 7, 1, 5 ]
vertex 4 -> Algebra 133 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 361 permutation [ 6, 2, 1, 7, 3, 4, 5 ]
Algebra 287
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 5 ], [ 4, 2 ], [ 4, 3 ], [ 5, 6 ], [ 6, 1 ], [ 6, 4 ], [ 7, 2 ]
Relations
[ 2, 6, 1 ]
[ 5, 6, 4, 3 ]
[ 2, 6, 4 ]
[ 3, 5, 6, 4 ]
[ 6, 4, 3, 5 ]
[ 1, 2, 6 ]
[ 6, 1, 2 ] - [ 6, 4, 2 ]
[ 4, 2, 6 ] - [ 4, 3, 5, 6 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 0 1 0)
(1 0 1 0 1 1 0)
(0 1 1 1 1 1 0)
(1 1 0 1 1 1 0)
(1 1 1 1 0 1 0)
(0 1 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 352 permutation [ 3, 1, 6, 4, 7, 2, 5 ]
vertex 2 -> Algebra 133 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 260 permutation [ 3, 6, 1, 4, 7, 2, 5 ]
vertex 5 -> Algebra 290 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 185 permutation [ 1, 3, 5, 4, 6, 2, 7 ]
Algebra 290
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 4, 2 ], [ 4, 3 ], [ 5, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ]
Relations
[ 2, 5, 1 ]
[ 2, 5, 4 ]
[ 3, 5, 4 ]
[ 1, 2, 5 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 1, 2 ] - [ 5, 4, 2 ]
[ 5, 4, 3 ] - [ 5, 6, 3 ]
[ 4, 2, 5 ] - [ 4, 3, 5 ]
Cartan matrix
(1 1 0 0 0 0 0)
(0 1 0 0 1 1 0)
(1 0 1 0 1 0 0)
(0 1 1 1 1 0 0)
(1 1 1 1 1 1 0)
(0 0 1 0 0 1 0)
(0 1 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 384 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 135 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 347 permutation [ 1, 3, 4, 5, 6, 2, 7 ]
vertex 6 -> Algebra 287 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 188 permutation [ 1, 3, 5, 4, 6, 2, 7 ]
Algebra 333
Quiver
[ 1, 4 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 5, 7 ], [ 6, 3 ], [ 7, 1 ]
Relations
[ 4, 3, 5, 7, 1 ]
[ 3, 5, 7, 1, 4 ]
[ 6, 3, 5 ]
[ 7, 1, 4, 3, 5 ]
[ 3, 5, 6 ]
[ 1, 4, 3, 5, 7 ]
[ 5, 6, 3 ] - [ 5, 7, 1, 4, 3 ]
Cartan matrix
(1 0 1 1 1 0 0)
(1 1 1 0 1 0 1)
(1 0 1 0 1 0 1)
(0 0 1 1 1 0 1)
(1 0 1 1 1 1 1)
(0 0 1 0 0 1 0)
(1 0 1 1 0 0 1)
Good mutations
vertex 2 -> Algebra 361 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 345 permutation [ 2, 1, 4, 5, 7, 3, 6 ]
vertex 4 -> Algebra 222 permutation [ 2, 3, 5, 6, 7, 1, 4 ]
vertex 7 -> Algebra 181 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 335
Quiver
[ 1, 3 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 2 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 3, 4, 1 ]
[ 5, 4, 1 ]
[ 3, 4, 2 ]
[ 2, 3, 4 ]
[ 6, 5, 4 ]
[ 5, 4, 6 ]
[ 4, 1, 3 ] - [ 4, 2, 3 ]
[ 1, 3, 4 ] - [ 1, 5, 4 ]
[ 4, 1, 5 ] - [ 4, 6, 5 ]
Cartan matrix
(1 0 1 1 1 0 0)
(0 1 1 0 0 0 0)
(0 0 1 1 0 1 1)
(1 1 1 1 1 1 1)
(0 1 0 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 338 permutation [ 5, 2, 3, 4, 1, 6, 7 ]
vertex 2 -> Algebra 385 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 7 -> Algebra 342 permutation [ 2, 5, 4, 1, 7, 6, 3 ]
Algebra 338
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 5 ], [ 4, 2 ], [ 4, 6 ], [ 5, 4 ], [ 6, 1 ], [ 6, 7 ]
Relations
[ 5, 4, 6, 1 ]
[ 3, 5, 4, 2 ]
[ 5, 4, 2, 3 ]
[ 2, 3, 5, 4 ]
[ 6, 1, 5, 4 ]
[ 1, 5, 4, 6 ]
[ 4, 2, 3, 5 ] - [ 4, 6, 1, 5 ]
Cartan matrix
(1 1 0 1 1 0 0)
(0 1 1 0 1 0 0)
(0 0 1 1 1 1 1)
(1 1 1 1 1 1 1)
(0 1 0 1 1 1 1)
(1 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 185 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 388 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 3 -> Algebra 341 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 200 permutation [ 2, 1, 5, 4, 6, 7, 3 ]
vertex 5 -> Algebra 335 permutation [ 5, 2, 3, 4, 1, 6, 7 ]
vertex 7 -> Algebra 352 permutation [ 2, 1, 5, 4, 7, 6, 3 ]
Algebra 341
Quiver
[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 6 ], [ 5, 2 ], [ 6, 1 ], [ 6, 7 ]
Relations
[ 3, 4, 6, 1 ]
[ 5, 2, 3 ]
[ 2, 3, 4 ]
[ 6, 1, 3, 4 ]
[ 2, 3, 5 ]
[ 1, 3, 4, 6 ]
[ 3, 4, 2 ] - [ 3, 5, 2 ]
[ 4, 2, 3 ] - [ 4, 6, 1, 3 ]
Cartan matrix
(1 1 1 1 1 0 0)
(0 1 1 0 0 0 0)
(0 1 1 1 1 1 1)
(1 1 1 1 0 1 1)
(0 1 0 0 1 0 0)
(1 0 1 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 188 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 380 permutation [ 3, 4, 1, 6, 7, 2, 5 ]
vertex 4 -> Algebra 345 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 338 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 376 permutation [ 1, 4, 3, 7, 5, 2, 6 ]
vertex 7 -> Algebra 384 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
Algebra 342
Quiver
[ 1, 7 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 4, 7 ], [ 5, 6 ], [ 6, 2 ], [ 7, 3 ]
Relations
[ 7, 3, 1 ]
[ 1, 7, 3 ]
[ 6, 2, 3 ]
[ 2, 3, 4 ]
[ 7, 3, 4 ]
[ 2, 3, 6 ]
[ 3, 4, 2 ] - [ 3, 6, 2 ]
[ 4, 2, 3 ] - [ 4, 7, 3 ]
[ 3, 1, 7 ] - [ 3, 4, 7 ]
Cartan matrix
(1 0 0 0 0 0 1)
(1 1 1 0 0 0 0)
(1 1 1 1 0 1 1)
(0 1 1 1 0 0 1)
(0 1 0 0 1 1 0)
(0 1 0 0 0 1 0)
(0 0 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 394 permutation [ 6, 4, 7, 3, 1, 2, 5 ]
vertex 4 -> Algebra 352 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 335 permutation [ 4, 1, 7, 3, 2, 6, 5 ]
vertex 6 -> Algebra 229 permutation [ 6, 4, 1, 3, 7, 2, 5 ]
Algebra 345
Quiver
[ 1, 4 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 2 ], [ 6, 1 ], [ 6, 3 ], [ 6, 7 ]
Relations
[ 4, 6, 1 ]
[ 3, 4, 5, 2 ]
[ 5, 2, 3, 4 ]
[ 2, 3, 4, 5 ]
[ 1, 4, 6 ]
[ 3, 4, 6 ]
[ 4, 5, 2, 3 ] - [ 4, 6, 3 ]
[ 6, 1, 4 ] - [ 6, 3, 4 ]
Cartan matrix
(1 1 0 1 1 0 0)
(0 1 1 1 0 0 0)
(0 0 1 1 1 0 0)
(0 1 1 1 1 1 1)
(0 1 1 0 1 0 0)
(1 0 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 194 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 341 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 200 permutation [ 2, 1, 4, 3, 6, 7, 5 ]
vertex 6 -> Algebra 333 permutation [ 2, 1, 6, 3, 4, 7, 5 ]
vertex 7 -> Algebra 353 permutation [ 2, 1, 4, 3, 7, 6, 5 ]
Algebra 346
Quiver
[ 1, 3 ], [ 1, 7 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 6, 1 ], [ 7, 6 ]
Relations
[ 7, 6, 1 ]
[ 3, 4, 5, 2 ]
[ 6, 1, 3 ]
[ 1, 3, 4 ]
[ 5, 2, 3, 4 ]
[ 2, 3, 4, 5 ]
[ 6, 1, 7 ]
[ 3, 4, 1 ] - [ 3, 6, 1 ]
[ 4, 1, 3 ] - [ 4, 5, 2, 3 ]
[ 1, 3, 6 ] - [ 1, 7, 6 ]
Cartan matrix
(1 0 1 0 0 1 1)
(1 1 1 1 0 1 0)
(1 0 1 1 1 1 0)
(1 1 1 1 1 1 1)
(0 1 1 0 1 1 0)
(1 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 361 permutation [ 2, 1, 6, 3, 4, 7, 5 ]
vertex 2 -> Algebra 376 permutation [ 4, 3, 1, 2, 7, 6, 5 ]
vertex 3 -> Algebra 231 permutation [ 4, 2, 1, 3, 7, 6, 5 ]
vertex 4 -> Algebra 195 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 234 permutation [ 2, 4, 6, 3, 1, 7, 5 ]
vertex 6 -> Algebra 194 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 347
Quiver
[ 1, 6 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 6, 3, 4, 1 ]
[ 3, 4, 5, 2 ]
[ 1, 6, 3, 4 ]
[ 5, 2, 3, 4 ]
[ 2, 3, 4, 5 ]
[ 3, 4, 1, 6 ]
[ 4, 1, 6, 3 ] - [ 4, 5, 2, 3 ]
Cartan matrix
(1 0 1 0 0 1 0)
(1 1 1 1 0 0 0)
(1 0 1 1 1 0 0)
(1 1 1 1 1 1 0)
(0 1 1 0 1 0 0)
(0 0 1 1 1 1 0)
(0 0 1 1 1 1 1)
Good mutations
vertex 1 -> Algebra 353 permutation [ 2, 1, 4, 3, 7, 6, 5 ]
vertex 2 -> Algebra 368 permutation [ 4, 7, 1, 2, 6, 3, 5 ]
vertex 3 -> Algebra 290 permutation [ 1, 6, 2, 3, 4, 5, 7 ]
vertex 4 -> Algebra 196 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 260 permutation [ 2, 4, 1, 3, 7, 6, 5 ]
vertex 7 -> Algebra 194 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 352
Quiver
[ 1, 7 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 6 ], [ 5, 6 ], [ 6, 2 ], [ 7, 3 ]
Relations
[ 7, 3, 4, 1 ]
[ 3, 4, 6, 2 ]
[ 1, 7, 3, 4 ]
[ 6, 2, 3, 4 ]
[ 2, 3, 4, 6 ]
[ 3, 4, 1, 7 ]
[ 4, 1, 7, 3 ] - [ 4, 6, 2, 3 ]
Cartan matrix
(1 0 1 0 0 0 1)
(1 1 1 1 0 0 0)
(1 0 1 1 0 1 0)
(1 1 1 1 0 1 1)
(0 1 1 0 1 1 0)
(0 1 1 0 0 1 0)
(0 0 1 1 0 1 1)
Good mutations
vertex 1 -> Algebra 397 permutation [ 6, 2, 7, 4, 1, 3, 5 ]
vertex 2 -> Algebra 287 permutation [ 2, 6, 1, 4, 7, 3, 5 ]
vertex 3 -> Algebra 342 permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex 4 -> Algebra 197 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 338 permutation [ 2, 1, 7, 4, 3, 6, 5 ]
vertex 6 -> Algebra 231 permutation [ 6, 2, 1, 4, 7, 3, 5 ]
vertex 7 -> Algebra 384 permutation [ 6, 2, 1, 4, 3, 7, 5 ]
Algebra 353
Quiver
[ 1, 4 ], [ 2, 3 ], [ 3, 6 ], [ 3, 7 ], [ 4, 3 ], [ 5, 6 ], [ 6, 2 ], [ 6, 4 ], [ 7, 1 ]
Relations
[ 4, 3, 7, 1 ]
[ 3, 6, 2 ]
[ 7, 1, 4, 3 ]
[ 2, 3, 6 ]
[ 4, 3, 6 ]
[ 1, 4, 3, 7 ]
[ 6, 2, 3 ] - [ 6, 4, 3 ]
[ 3, 6, 4 ] - [ 3, 7, 1, 4 ]
Cartan matrix
(1 0 1 1 0 0 0)
(1 1 1 0 0 0 1)
(1 0 1 1 0 1 1)
(0 0 1 1 0 0 1)
(0 1 1 1 1 1 1)
(0 1 1 1 0 1 1)
(1 0 0 1 0 0 1)
Good mutations
vertex 2 -> Algebra 347 permutation [ 2, 1, 4, 3, 7, 6, 5 ]
vertex 4 -> Algebra 384 permutation [ 6, 2, 1, 4, 3, 7, 5 ]
vertex 5 -> Algebra 345 permutation [ 2, 1, 4, 3, 7, 6, 5 ]
vertex 7 -> Algebra 197 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 361
Quiver
[ 1, 4 ], [ 2, 3 ], [ 2, 5 ], [ 4, 2 ], [ 5, 6 ], [ 5, 7 ], [ 6, 2 ], [ 7, 1 ]
Relations
[ 4, 2, 5, 7, 1 ]
[ 2, 5, 7, 1, 4 ]
[ 6, 2, 5 ]
[ 7, 1, 4, 2, 5 ]
[ 2, 5, 6 ]
[ 1, 4, 2, 5, 7 ]
[ 5, 6, 2 ] - [ 5, 7, 1, 4, 2 ]
Cartan matrix
(1 1 1 1 1 0 0)
(1 1 1 0 1 0 1)
(0 0 1 0 0 0 0)
(0 1 1 1 1 0 1)
(1 1 1 1 1 1 1)
(0 1 1 0 0 1 0)
(1 1 1 1 0 0 1)
Good mutations
vertex 2 -> Algebra 346 permutation [ 2, 1, 4, 5, 7, 3, 6 ]
vertex 3 -> Algebra 333 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 280 permutation [ 3, 2, 5, 6, 7, 1, 4 ]
vertex 7 -> Algebra 213 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 368
Quiver
[ 1, 3 ], [ 1, 7 ], [ 2, 5 ], [ 3, 5 ], [ 4, 7 ], [ 5, 6 ], [ 6, 1 ], [ 6, 4 ], [ 7, 6 ]
Relations
[ 3, 5, 6, 1 ]
[ 7, 6, 1 ]
[ 5, 6, 1, 3 ]
[ 7, 6, 4 ]
[ 6, 1, 3, 5 ]
[ 4, 7, 6 ]
[ 1, 3, 5, 6 ] - [ 1, 7, 6 ]
[ 6, 1, 7 ] - [ 6, 4, 7 ]
Cartan matrix
(1 0 1 0 1 1 1)
(1 1 0 1 1 1 1)
(0 0 1 1 1 1 0)
(0 0 0 1 0 0 1)
(1 0 0 1 1 1 1)
(1 0 1 1 0 1 1)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 254 permutation [ 3, 6, 4, 1, 7, 5, 2 ]
vertex 2 -> Algebra 252 permutation [ 3, 6, 4, 1, 7, 5, 2 ]
vertex 4 -> Algebra 347 permutation [ 3, 4, 6, 1, 7, 5, 2 ]
vertex 7 -> Algebra 390 permutation [ 1, 3, 2, 6, 5, 7, 4 ]
Algebra 376
Quiver
[ 1, 3 ], [ 1, 7 ], [ 2, 1 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 3, 5 ], [ 4, 7 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ]
Relations
[ 3, 2, 1 ]
[ 7, 2, 1 ]
[ 4, 7, 2 ]
[ 6, 3, 2 ]
[ 5, 6, 3 ]
[ 7, 2, 4 ]
[ 6, 3, 5 ]
[ 1, 3, 2 ] - [ 1, 7, 2 ]
[ 2, 1, 3 ] - [ 2, 6, 3 ]
[ 3, 2, 6 ] - [ 3, 5, 6 ]
[ 2, 1, 7 ] - [ 2, 4, 7 ]
Cartan matrix
(1 1 1 0 1 1 1)
(1 1 1 1 0 1 1)
(0 1 1 1 1 1 0)
(0 0 0 1 0 0 1)
(0 0 0 0 1 1 0)
(0 0 1 0 0 1 0)
(0 1 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 253 permutation [ 3, 2, 4, 1, 7, 6, 5 ]
vertex 2 -> Algebra 222 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 346 permutation [ 3, 4, 2, 1, 7, 6, 5 ]
vertex 6 -> Algebra 252 permutation [ 3, 2, 4, 1, 7, 6, 5 ]
vertex 7 -> Algebra 341 permutation [ 1, 6, 3, 2, 5, 7, 4 ]
Algebra 380
Quiver
[ 1, 6 ], [ 2, 4 ], [ 3, 1 ], [ 4, 3 ], [ 4, 5 ], [ 6, 2 ], [ 6, 7 ]
Relations
[ 6, 2, 4, 3, 1 ]
[ 4, 3, 1, 6, 2 ]
[ 1, 6, 2, 4, 3 ]
[ 3, 1, 6, 2, 4 ]
[ 2, 4, 3, 1, 6 ]
Cartan matrix
(1 1 0 1 1 1 1)
(1 1 1 1 1 0 0)
(1 1 1 0 0 1 1)
(1 0 1 1 1 1 1)
(0 0 0 0 1 0 0)
(0 1 1 1 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 252 permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex 5 -> Algebra 401 permutation [ 4, 3, 1, 2, 6, 7, 5 ]
vertex 6 -> Algebra 341 permutation [ 3, 6, 1, 2, 7, 4, 5 ]
vertex 7 -> Algebra 390 permutation [ 3, 1, 7, 2, 6, 4, 5 ]
Algebra 384
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 4, 1 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ]
Relations
[ 2, 5, 4, 1 ]
[ 5, 4, 1, 2 ]
[ 1, 2, 5, 4 ]
[ 3, 5, 4 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 4, 3 ] - [ 5, 6, 3 ]
[ 4, 1, 2, 5 ] - [ 4, 3, 5 ]
Cartan matrix
(1 1 0 0 1 1 0)
(0 1 1 1 1 1 0)
(0 0 1 0 1 0 0)
(1 1 1 1 1 0 0)
(1 0 1 1 1 1 0)
(0 0 1 0 0 1 0)
(1 1 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 234 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 290 permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 401 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 4 -> Algebra 353 permutation [ 3, 2, 5, 4, 7, 1, 6 ]
vertex 6 -> Algebra 352 permutation [ 3, 2, 5, 4, 7, 1, 6 ]
vertex 7 -> Algebra 341 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
Algebra 385
Quiver
[ 1, 2 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 2, 3, 4, 1 ]
[ 5, 4, 1 ]
[ 3, 4, 1, 2 ]
[ 4, 1, 2, 3 ]
[ 6, 5, 4 ]
[ 5, 4, 6 ]
[ 1, 2, 3, 4 ] - [ 1, 5, 4 ]
[ 4, 1, 5 ] - [ 4, 6, 5 ]
Cartan matrix
(1 1 1 1 1 0 0)
(0 1 1 1 0 1 1)
(1 0 1 1 1 1 1)
(1 1 0 1 1 1 1)
(0 0 0 1 1 0 0)
(0 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 388 permutation [ 5, 2, 3, 4, 1, 6, 7 ]
vertex 3 -> Algebra 335 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 5 -> Algebra 237 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 394 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
Algebra 387
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 2, 3, 4, 5, 1 ]
[ 3, 4, 5, 1, 2 ]
[ 4, 5, 1, 2, 3 ]
[ 5, 1, 2, 3, 4 ]
[ 1, 2, 3, 4, 5 ]
Cartan matrix
(1 1 1 1 0 0 0)
(0 1 1 1 1 1 0)
(1 0 1 1 1 1 0)
(1 1 0 1 1 1 0)
(1 1 1 0 1 1 0)
(0 0 0 0 0 1 0)
(0 0 0 0 0 1 1)
Good mutations
vertex 5 -> Algebra 394 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
vertex 6 -> Algebra 251 permutation [ 5, 1, 2, 4, 3, 6, 7 ]
vertex 7 -> Algebra 237 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 388
Quiver
[ 1, 5 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 4, 6 ], [ 5, 4 ], [ 6, 1 ], [ 6, 7 ]
Relations
[ 5, 4, 6, 1 ]
[ 3, 4, 2 ]
[ 5, 4, 2 ]
[ 4, 2, 3 ]
[ 6, 1, 5, 4 ]
[ 1, 5, 4, 6 ]
[ 2, 3, 4 ] - [ 2, 5, 4 ]
[ 4, 2, 5 ] - [ 4, 6, 1, 5 ]
Cartan matrix
(1 0 0 1 1 0 0)
(0 1 1 1 1 1 1)
(1 0 1 1 0 1 1)
(1 1 0 1 1 1 1)
(0 0 0 1 1 1 1)
(1 0 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 390 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 3 -> Algebra 338 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 5 -> Algebra 385 permutation [ 5, 2, 3, 4, 1, 6, 7 ]
vertex 7 -> Algebra 397 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
Algebra 390
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 4, 6 ], [ 5, 4 ], [ 6, 1 ], [ 6, 7 ]
Relations
[ 2, 5, 4, 6, 1 ]
[ 5, 4, 6, 1, 2 ]
[ 6, 1, 2, 5, 4 ]
[ 4, 6, 1, 2, 5 ]
[ 1, 2, 5, 4, 6 ]
Cartan matrix
(1 1 0 1 1 0 0)
(0 1 0 1 1 1 1)
(1 0 1 1 1 1 1)
(1 1 0 1 0 1 1)
(1 0 0 1 1 1 1)
(1 1 0 0 1 1 1)
(0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 380 permutation [ 2, 4, 1, 6, 7, 5, 3 ]
vertex 5 -> Algebra 388 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 6 -> Algebra 368 permutation [ 1, 3, 2, 7, 5, 4, 6 ]
vertex 7 -> Algebra 400 permutation [ 6, 1, 2, 4, 3, 5, 7 ]
Algebra 392
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 1 ], [ 5, 4 ], [ 6, 1 ], [ 7, 6 ]
Relations
[ 2, 3, 5, 4, 1 ]
[ 3, 5, 4, 1, 2 ]
[ 5, 4, 1, 2, 3 ]
[ 1, 2, 3, 5, 4 ]
[ 4, 1, 2, 3, 5 ]
Cartan matrix
(1 1 1 0 1 0 0)
(0 1 1 1 1 0 0)
(1 0 1 1 1 0 0)
(1 1 1 1 0 0 0)
(1 1 0 1 1 0 0)
(1 1 1 0 1 1 0)
(1 1 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 254 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 7 -> Algebra 251 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 394
Quiver
[ 1, 6 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 4, 1 ], [ 4, 2 ], [ 5, 4 ], [ 6, 4 ], [ 7, 1 ]
Relations
[ 6, 4, 1 ]
[ 3, 5, 4, 2 ]
[ 6, 4, 2 ]
[ 5, 4, 2, 3 ]
[ 1, 6, 4 ]
[ 4, 2, 3, 5 ]
[ 2, 3, 5, 4 ] - [ 2, 6, 4 ]
[ 4, 1, 6 ] - [ 4, 2, 6 ]
Cartan matrix
(1 0 0 0 0 1 0)
(0 1 1 1 1 1 0)
(1 0 1 1 1 0 0)
(1 1 1 1 0 1 0)
(1 1 0 1 1 1 0)
(0 0 0 1 0 1 0)
(1 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 253 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 397 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex 5 -> Algebra 342 permutation [ 5, 6, 4, 2, 7, 1, 3 ]
vertex 6 -> Algebra 387 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
vertex 7 -> Algebra 385 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
Algebra 397
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 5 ], [ 3, 6 ], [ 4, 1 ], [ 4, 3 ], [ 5, 4 ], [ 6, 4 ], [ 7, 1 ]
Relations
[ 2, 6, 4, 1 ]
[ 6, 4, 1, 2 ]
[ 5, 4, 3 ]
[ 6, 4, 3 ]
[ 1, 2, 6, 4 ]
[ 4, 3, 5 ]
[ 3, 5, 4 ] - [ 3, 6, 4 ]
[ 4, 1, 2, 6 ] - [ 4, 3, 6 ]
Cartan matrix
(1 1 0 0 0 1 0)
(0 1 0 1 0 1 0)
(1 0 1 1 1 1 0)
(1 1 1 1 0 1 0)
(1 1 0 1 1 0 0)
(1 0 0 1 0 1 0)
(1 1 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 257 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 400 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 5 -> Algebra 352 permutation [ 5, 2, 6, 4, 7, 1, 3 ]
vertex 6 -> Algebra 394 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex 7 -> Algebra 388 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
Algebra 400
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 6 ], [ 4, 1 ], [ 5, 6 ], [ 6, 4 ], [ 7, 1 ]
Relations
[ 2, 3, 6, 4, 1 ]
[ 3, 6, 4, 1, 2 ]
[ 6, 4, 1, 2, 3 ]
[ 1, 2, 3, 6, 4 ]
[ 4, 1, 2, 3, 6 ]
Cartan matrix
(1 1 1 0 0 1 0)
(0 1 1 1 0 1 0)
(1 0 1 1 0 1 0)
(1 1 1 1 0 0 0)
(1 1 0 1 1 1 0)
(1 1 0 1 0 1 0)
(1 1 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 260 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 401 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 6 -> Algebra 397 permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex 7 -> Algebra 390 permutation [ 2, 3, 5, 4, 6, 1, 7 ]
Algebra 401
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 1 ], [ 5, 4 ], [ 5, 6 ], [ 7, 1 ]
Relations
[ 2, 3, 5, 4, 1 ]
[ 3, 5, 4, 1, 2 ]
[ 5, 4, 1, 2, 3 ]
[ 1, 2, 3, 5, 4 ]
[ 4, 1, 2, 3, 5 ]
Cartan matrix
(1 1 1 0 1 1 0)
(0 1 1 1 1 1 0)
(1 0 1 1 1 1 0)
(1 1 1 1 0 0 0)
(1 1 0 1 1 1 0)
(0 0 0 0 0 1 0)
(1 1 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 263 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 5 -> Algebra 384 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 400 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 380 permutation [ 3, 4, 2, 1, 7, 5, 6 ]