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arXiv · 1909.05340

Continuous cluster categories II: continuous cluster-tilted categories

Kiyoshi Igusa·Gordana Todorov
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Abstract

We show that the quotient of the continuous cluster category $\mathcal C_\pi$ 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 $A$. These results will be generalized in a series of forthcoming joint papers of the two authors with Job Rock.

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Kiyoshi Igusa, Gordana Todorov. 2019-09-11. Continuous cluster categories II: continuous cluster-tilted categories. https://arxiv.org/abs/1909.05340

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