COMPONENT CLUSTERS FOR ACYCLIC QUIVERS

The theory of Caldero-Chapoton algebras of Cerulli Irelli, Labardini-Fragoso and Schroer (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.