The cluster category of a canonical algebra
Representation Theory
2020-09-28 v3
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 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.
Keywords
Cite
@article{arxiv.0801.4540,
title = {The cluster category of a canonical algebra},
author = {Michael Barot and Dirk Kussin and Helmut Lenzing},
journal= {arXiv preprint arXiv:0801.4540},
year = {2020}
}
Comments
16 pages. A few minor changes, one reference added. To appear in Trans. Amer. Math. Soc