Component clusters for acyclic quivers
Tom 144 / 2016
Colloquium Mathematicum 144 (2016), 245-264
MSC: Primary 13F60; Secondary 16G20.
DOI: 10.4064/cm6691-9-2015
Opublikowany online: 23 March 2016
Streszczenie
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.
