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Properties of minimal mutation-infinite quivers | | John W. Lawson
; Matthew R. Mills
; | | Date: |
26 Oct 2016 | | Abstract: | We study properties of minimal mutation-infinite quivers. In particular we
show that every minimal-mutation infinite quiver of at least rank 4 is Louise
and has a maximal green sequence. It then follows that the cluster algebras
generated by these quivers are locally acyclic and hence equal to their upper
cluster algebra. We also study which quivers in a mutation-class have a maximal
green sequence. For any rank 3 quiver there are at most 6 quivers in its
mutation class that admit a maximal green sequence. We also show that for every
rank 4 minimal mutation-infinite quiver there is a finite connected subgraph of
the unlabelled exchange graph consisting of quivers that admit a maximal green
sequence. | | Source: | arXiv, 1610.8333 | | Services: | Forum | Review | PDF | Favorites | |
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