Continuous cluster categories II: continuous cluster-tilted categories
Representation Theory
2019-09-13 v1
Abstract
We show that the quotient of the continuous cluster category modulo the additive subcategory generated by any cluster is an abelian category and we show that it is isomorphic to the category of infinite length modules over the endomorphism ring of the cluster. These theorems extend the theorems of Caldero-Chapoton-Schiffler and Buan-Marsh-Reiten for cluster categories to the continuous cluster category of type . These results will be generalized in a series of forthcoming joint papers of the two authors with Job Rock.
Cite
@article{arxiv.1909.05340,
title = {Continuous cluster categories II: continuous cluster-tilted categories},
author = {Kiyoshi Igusa and Gordana Todorov},
journal= {arXiv preprint arXiv:1909.05340},
year = {2019}
}
Comments
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