The Existence of a Maximal Green Sequence is not Invariant under Quiver Mutation

Greg Muller

Abstract


This note provides a quiver which does not admit a maximal green sequence, but which is mutation-equivalent to a quiver which does admit a maximal green sequence. The proof uses the `scattering diagrams' of Gross-Hacking-Keel-Kontsevich to show that a maximal green sequence for a quiver determines a maximal green sequence for any induced subquiver.

Keywords


Cluster algebras; Quiver mutation

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