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

 

Calabi-Yau objects in triangulated categories


Authors: Claude Cibils and Pu Zhang
Journal: Trans. Amer. Math. Soc. 361 (2009), 6501-6519
MSC (2000): Primary 18E30; Secondary 16G20, 16G70, 16E30, 18G20
Published electronically: July 24, 2009
MathSciNet review: 2538602
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Abstract: We introduce the Calabi-Yau (CY) objects in a Hom-finite Krull-Schmidt triangulated $ k$-category, and notice that the structure of the minimal, consequently all the CY objects, can be described. The relation between indecomposable CY objects and Auslander-Reiten triangles is provided. Finally we classify all the CY modules of self-injective Nakayama algebras, determining in this way the self-injective Nakayama algebras admitting indecomposable CY modules.


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Additional Information

Claude Cibils
Affiliation: Institut de Mathématiques et de Modélisation de Montpellier-I3M, Université Montpellier 2, F-34095, Montpellier Cedex 5, France
Email: Claude.Cibils@math.univ-montp2.fr

Pu Zhang
Affiliation: Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
Email: pzhang@sjtu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04682-0
PII: S 0002-9947(09)04682-0
Keywords: Serre functor, Calabi-Yau object, Auslander-Reiten triangle, stable module category, self-injective Nakayama algebra
Received by editor(s): November 16, 2007
Published electronically: July 24, 2009
Additional Notes: The second author was supported by the Chinese Natural Science Foundation for Distinguished Young Scholars (Grant No. 10725104) and the CNRS of France.
Pu Zhang is the corresponding author for this paper.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.