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

   

 

Cluster-tilted algebras


Authors: Aslak Bakke Buan, Robert J. Marsh and Idun Reiten
Journal: Trans. Amer. Math. Soc. 359 (2007), 323-332
MSC (2000): Primary 16G20, 16G70; Secondary 16E99, 16S99
Published electronically: July 21, 2006
MathSciNet review: 2247893
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Abstract: We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation theory of hereditary algebras. As an application of this, we prove a generalised version of so-called APR-tilting.


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Additional Information

Aslak Bakke Buan
Affiliation: Institutt for Matematiske Fag, Norges Teknisk-Naturvitenskapelige Universitet, N-7491 Trondheim, Norway
Email: aslakb@math.ntnu.no

Robert J. Marsh
Affiliation: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, England
Email: rjm25@mcs.le.ac.uk

Idun Reiten
Affiliation: Institutt for Matematiske Fag, Norges Teknisk-Naturvitenskapelige Universitet, N-7491 Trondheim, Norway
Email: idunr@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03879-7
PII: S 0002-9947(06)03879-7
Keywords: APR-tilting theory, tilting module, complement, approximation theory, derived category, cluster category
Received by editor(s): February 26, 2004
Received by editor(s) in revised form: November 12, 2004
Published electronically: July 21, 2006
Additional Notes: The first author was supported by a grant from the Norwegian Research Council. The second author was supported by a Leverhulme Fellowship and by the Norwegian Research Council
Dedicated: Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday
Article copyright: © Copyright 2006 A. B. Buan, R. J. Marsh and I. Reiten