Vol. 290, No. 2, 2017

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ISSN: 0030-8730
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
Milestones
Received: 12 October 2016
Revised: 17 February 2017
Accepted: 27 February 2017
Published: 25 July 2017
Authors
Xingting Wang
Department of Mathematics
Temple University
Philadelphia, PA 19122
United States
Xiaolan Yu
Department of Mathematics
Hangzhou Normal University
310036 Hangzhou
China
Yinhuo Zhang
Department of Mathematics and Statistics
University of Hasselt
Universitaire Campus
3590 Diepeenbeek
Belgium