Cluster structures from 2-Calabi-Yau categories with loops
Representation Theory
2020-12-21 v1
Abstract
We generalise the notion of cluster structures from the work of Buan-Iyama-Reiten-Scott to include situations where the endomorphism rings of the clusters may have loops. We show that in a Hom-finite 2-Calabi-Yau category, the set of maximal rigid objects satisfies these axioms whenever there are no 2-cycles in the quivers of their endomorphism rings. We apply this result to the cluster category of a tube, and show that this category forms a good model for the combinatorics of a type B cluster algebra.
Cite
@article{arxiv.0810.3132,
title = {Cluster structures from 2-Calabi-Yau categories with loops},
author = {Aslak Bakke Buan and Bethany Marsh and Dagfinn F. Vatne},
journal= {arXiv preprint arXiv:0810.3132},
year = {2020}
}
Comments
15 pages, 7 figures