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INVARIANCE OF THE GERSTENHABER ALGEBRA STRUCTURE ON TATE-HOCHSCHILD COHOMOLOGY

Part of: Abelian categories Homological methods Homological algebra Modules, bimodules and ideals

Published online by Cambridge University Press:  15 July 2019

Zhengfang Wang
Zhengfang Wang*
Affiliation:
Beijing International Center for Mathematical Research (BICMR), Peking University, No. 5 Yiheyuan Road Haidian District, Beijing100871, P.R. China Université Paris Diderot-Paris 7, Institut de Mathématiques de Jussieu-Paris Rive Gauche CNRS UMR 7586, Bâtiment Sophie Germain, Case 7012, 75205 Paris Cedex 13, France (wangzhengfang@bicmr.pku.edu.cn)
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Abstract

Keller proved in 1999 that the Gerstenhaber algebra structure on the Hochschild cohomology of an algebra is an invariant of the derived category. In this paper, we adapt his approach to show that the Gerstenhaber algebra structure on the Tate–Hochschild cohomology of an algebra is preserved under singular equivalences of Morita type with level, a notion introduced by the author in previous work.

Keywords

Gerstenhaber algebraSingularity categoryTate–Hochschild cohomology

MSC classification

Primary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
Secondary: 18E30: Derived categories, triangulated categories 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality 18G10: Resolutions; derived functors
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 3 , May 2021 , pp. 893 - 928
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Copyright
© Cambridge University Press 2019

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