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Component clusters for acyclic quivers

Volume 144 / 2016

Sarah Scherotzke Colloquium Mathematicum 144 (2016), 245-264 MSC: Primary 13F60; Secondary 16G20. DOI: 10.4064/cm6691-9-2015 Published online: 23 March 2016

Abstract

The theory of Caldero–Chapoton algebras of Cerulli Irelli, Labardini-Fragoso and Schröer (2015) leads to a refinement of the notions of cluster variables and clusters, via so-called component clusters. We compare component clusters to classical clusters for the cluster algebra of an acyclic quiver. We propose a definition of mutation between component clusters and determine the mutation relations of component clusters for affine quivers. In the case of a wild quiver, we provide bounds for the size of component clusters.

Authors

  • Sarah ScherotzkeInstitute of Mathematics
    University of Bonn
    D-53115 Bonn, Germany
    e-mail

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