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A construction of derived equivalent pairs of symmetric algebras


Author: Alex Dugas
Journal: Proc. Amer. Math. Soc. 143 (2015), 2281-2300
MSC (2010): Primary 16G10, 18E30, 16E35
DOI: https://doi.org/10.1090/S0002-9939-2015-12655-X
Published electronically: February 16, 2015
MathSciNet review: 3326012
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Abstract: Recently, Hu and Xi have exhibited derived equivalent endomorphism rings arising from (relative) almost split sequences as well as AR-triangles in triangulated categories. We present a broader class of triangles (in algebraic triangulated categories) for which the endomorphism rings of different terms are derived equivalent. We then study applications involving 0-Calabi-Yau triangulated categories. In particular, applying our results in the category of perfect complexes over a symmetric algebra gives a nice way of producing pairs of derived equivalent symmetric algebras. Included in the examples we work out are some of the algebras of dihedral type with two or three simple modules. We also apply our results to stable categories of Cohen-Macaulay modules over odd-dimensional Gorenstein hypersurfaces having an isolated singularity.


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Additional Information

Alex Dugas
Affiliation: Department of Mathematics, University of the Pacific, 3601 Pacific Avenue, Stockton, California 95211
Email: adugas@pacific.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12655-X
Keywords: Derived equivalence, tilting complex, symmetric algebra
Received by editor(s): May 31, 2011
Received by editor(s) in revised form: November 26, 2013
Published electronically: February 16, 2015
Communicated by: Harm Derksen
Article copyright: © Copyright 2015 American Mathematical Society

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