A construction of derived equivalent pairs of symmetric algebras
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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.References
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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
- 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
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3326012