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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The cluster category of a canonical algebra


Authors: M. Barot, D. Kussin and H. Lenzing
Journal: Trans. Amer. Math. Soc. 362 (2010), 4313-4330
MSC (2000): Primary 16G20, 18E30
Published electronically: March 5, 2010
MathSciNet review: 2608408
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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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Additional Information

M. Barot
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, C.P. 04510, Mexico
Email: barot@matem.unam.mx

D. Kussin
Affiliation: Institut für Mathematik, Universität Paderborn, 33095 Paderborn, Germany
Address at time of publication: Fakultät für Mathematik, Universität Bielefeld, P. O. Box 100131, 33501 Bielefeld, Germany
Email: dirk@math.uni-paderborn.de, dkussin@math.uni-bielefeld.de

H. Lenzing
Affiliation: Institut für Mathematik, Universität Paderborn, 33095 Paderborn, Germany
Email: helmut@math.uni-paderborn.de

DOI: http://dx.doi.org/10.1090/S0002-9947-10-04998-6
PII: S 0002-9947(10)04998-6
Received by editor(s): August 12, 2008
Published electronically: March 5, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.