Cohomology of Graded Twisting of Hopf Algebras - Xiaolan Yu; Jingting Yang (Mathematics, 2023)
Let A be a Hopf algebra and B a graded twisting of A by a finite abelian group <semantics>Γ</semantics>. 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.