Calabi–Yau property under monoidal Morita–Takeuchi equivalence

Xingting Wang, Xiaolan Yu and Yinhuo Zhang

Vol. 290 (2017), No. 2, 481–510

DOI: 10.2140/pjm.2017.290.481

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

Milestones

Received: 12 October 2016 (corresponding author: Xiaolan Yu)

Revised: 17 February 2017

Accepted: 27 February 2017

Published: 25 July 2017