#### Vol. 290, No. 2, 2017

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Calabi–Yau property under monoidal Morita–Takeuchi equivalence

### Xingting Wang, Xiaolan Yu and Yinhuo Zhang

Vol. 290 (2017), No. 2, 481–510
##### Abstract

Let $H$ and $L$ be two Hopf algebras such that their comodule categories are monoidally equivalent. We prove that if $H$ is a twisted Calabi–Yau (CY) Hopf algebra, then $L$ is a twisted CY algebra when it is homologically smooth. In particular, if $H$ is a Noetherian twisted CY Hopf algebra and $L$ has finite global dimension, then $L$ is a twisted CY algebra.

##### Keywords
Morita–Takeuchi equivalence, Calabi–Yau algebra, cogroupoid
##### Mathematical Subject Classification 2010
Primary: 16E65, 16W30, 16W35