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arXiv · 0810.3132

Cluster structures from 2-Calabi-Yau categories with loops

Aslak Bakke Buan·Bethany Marsh·Dagfinn F. Vatne
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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.

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BibTeXRIS

Aslak Bakke Buan, Bethany Marsh, Dagfinn F. Vatne. 2008-10-17. Cluster structures from 2-Calabi-Yau categories with loops. https://arxiv.org/abs/0810.3132

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