Cohomology of Graded Twisting of Hopf Algebras

Xiaolan Yu () and Jingting Yang
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Xiaolan Yu: Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China
Jingting Yang: Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China

Mathematics, 2023, vol. 11, issue 12, 1-18

Abstract: Let A be a Hopf algebra and B a graded twisting of A by a finite abelian group Γ . Then, categories of comodules over A and B are equivalent (but they are not necessarily monoidally equivalent). We show the relation between the Hochschild cohomology of A and B explicitly. This partially answer a question raised by Bichon. As an application, we prove that A is a twisted Calabi–Yau Hopf algebra if and only if B is a twisted Calabi–Yau algebra, and give the relation between their Nakayama automorphisms.

Keywords: graded twisting; Hochschild cohomology; Calabi–Yau algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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