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Triangulated categories of Gorenstein cyclic quotient singularities


Author: Kazushi Ueda
Journal: Proc. Amer. Math. Soc. 136 (2008), 2745-2747
MSC (2000): Primary 18E30; Secondary 16G20
DOI: https://doi.org/10.1090/S0002-9939-08-09470-7
Published electronically: April 3, 2008
MathSciNet review: 2399037
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Abstract: We prove there is an equivalence of derived categories between Orlov's triangulated category of singularities for a Gorenstein cyclic quotient singularity and the derived category of representations of a quiver with relations, which is obtained from a McKay quiver by removing one vertex and half of the arrows. This result produces examples of distinct quivers with relations which have equivalent derived categories of representations.


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Additional Information

Kazushi Ueda
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan
Email: kazushi@math.sci.osaka-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-08-09470-7
Received by editor(s): July 6, 2006
Received by editor(s) in revised form: October 6, 2006, and July 8, 2007
Published electronically: April 3, 2008
Additional Notes: The author was supported by the 21st Century COE Program of Osaka University.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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