Cluster structures from 2-Calabi–Yau categories with loops

By Aslak Bakke Buan, Robert J. Marsh, D. Vatne. 2008

56 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/860d7fe257d4bb5651dc20ef273c818943dd73d5

Citations in the corpus

• Maximal rigid subcategories in 2-Calabi-Yau triangulated categories (2010, unknown): “It was proved recently by Buan-Marsh-Vatne in [BMV] that cluster tubes contain maximal rigid objects, none of them are cluster tilting.”