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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6691-9-2015,
author = {Sarah Scherotzke},
title = {Component clusters for acyclic quivers},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {245-264},
zbl = {06575003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6691-9-2015}
}
Sarah Scherotzke. Component clusters for acyclic quivers. Colloquium Mathematicae, Tome 144 (2016) pp. 245-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6691-9-2015/