The cluster category of a canonical algebra

Details The cluster category of a canonical algebra The cluster category of a canonical algebra

2008-01-29

arxiv.org/abs/0801.4540v3

Mathematics

Representation Theory

16 pages. A few minor changes, one reference added. To appear in Trans. Amer. Math. Soc

Scientific paper

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 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-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 X is non-negative, or equivalently, if A is of tame (domestic or tubular) representation type.

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