The cluster category of a canonical algebra

Barot, M.; Kussin, D.; Lenzing, H.

doi:10.1090/S0002-9947-10-04998-6

The cluster category of a canonical algebra
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by M. Barot, D. Kussin and H. Lenzing

Trans. Amer. Math. Soc. 362 (2010), 4313-4330

DOI: https://doi.org/10.1090/S0002-9947-10-04998-6

Published electronically: March 5, 2010

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Abstract:

We study the cluster category of a canonical algebra $A$ in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line $\mathbb {X}$. As an application we determine the automorphism group of the cluster category and show that the cluster-tilting objects form a cluster structure in the sense of Buan, Iyama, Reiten and Scott. The tilting graph of the sheaf category always coincides with the tilting or exchange graph of the cluster category. We show that this graph is connected if the Euler characteristic of $\mathbb {X}$ is non-negative, or equivalently, if $A$ is of tame (domestic or tubular) representation type.

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