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Stable equivalences of Morita type do not preserve tensor products and trivial extensions of algebras


Authors: Yuming Liu, Guodong Zhou and Alexander Zimmermann
Journal: Proc. Amer. Math. Soc. 145 (2017), 1881-1890
MSC (2010): Primary 16G10, 20C05
DOI: https://doi.org/10.1090/proc/13448
Published electronically: January 25, 2017
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Abstract: It is well known that derived equivalences preserve tensor products and trivial extensions. We disprove both constructions for stable equivalences of Morita type.


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Yuming Liu
Affiliation: School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, People’s Republic of China
Email: ymliu@bnu.edu.cn

Guodong Zhou
Affiliation: Department of Mathematics, Shanghai Key laboratory of PMMP, East China Normal University, Dong Chuan Road 500, Shanghai 200241, People’s Republic of China
Email: gdzhou@math.ecnu.edu.cn

Alexander Zimmermann
Affiliation: Université de Picardie, Faculté de Mathématiques et LAMFA (UMR 7352 du CNRS), 33 rue St Leu, F-80039 Amiens Cedex 1, France
Email: Alexander.Zimmermann@u-picardie.fr

DOI: https://doi.org/10.1090/proc/13448
Keywords: Stable equivalence of Morita type, tensor product, trivial extension, center, stable center
Received by editor(s): August 29, 2014
Received by editor(s) in revised form: July 27, 2015, and June 27, 2016
Published electronically: January 25, 2017
Additional Notes: The authors were supported by the exchange program STIC-Asie ‘ESCAP’ financed by the French Ministry of Foreign Affairs
The first author was supported by the NCET Program from MOE of China, by NSFC (No. 11171325, No. 11331006), and by the Fundamental Research Funds for the Central Universities
The second author was supported by NSFC (No. 11671139) and by STCSM (No. 13dz2260400)
Communicated by: Harm Derksen
Article copyright: © Copyright 2017 American Mathematical Society