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Cluster-tilted algebras
Author(s):
Aslak
Bakke Buan;
Robert
J.
Marsh;
Idun
Reiten
Journal:
Trans. Amer. Math. Soc.
359
(2007),
323-332.
MSC (2000):
Primary 16G20, 16G70;
Secondary 16E99, 16S99
Posted:
July 21, 2006
MathSciNet review:
2247893
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References |
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Additional information
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.
References:
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- Brenner, S., Butler, M. C. R., Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors, Representation Theory, II (Proc. Second Internat. Conf., Carleton Univ., Ottawa, Ont., 1979), Lecture Notes in Math., 832, Springer, Berlin-New York (1980), 103-169. MR 0607151 (83e:16031)
- [BMRRT]
- Buan, A., Marsh, R., Reineke, M., Reiten, I., Todorov, G., Tilting theory and cluster combinatorics, preprint math.RT/0402054, (2004), to appear in Adv. Math.
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- Caldero, P., Chapoton, F., and Schiffler, R., Quivers with relations arising from clusters (
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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:
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
Posted:
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
Copyright of article:
Copyright
2006,
A. B. Buan, R. J. Marsh and I. Reiten
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