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tate–hochschild cohomology

Journal of the Institute of Mathematics of Jussieu (1)

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INVARIANCE OF THE GERSTENHABER ALGEBRA STRUCTURE ON TATE-HOCHSCHILD COHOMOLOGY
Part of
Zhengfang Wang
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 3 / May 2021

Published online by Cambridge University Press:

15 July 2019, pp. 893-928

Print publication:

May 2021
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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.