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

  • Greg Muller
Keywords: Cluster algebras, Quiver mutation

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.
Published
2016-06-10
Article Number
P2.47