Calabi-Yau property under monoidal Morita-Takeuchi equivalence

2016/10/06 by Wang, Xingting, Yu, Xiaolan, Zhang, Yinhuo
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1610.01881

Abstract

Let H and L be two Hopf algebras such that their comodule categories are monoidal 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. Especially, if H is a Noetherian twisted CY Hopf algebra and L has finite global dimension, then L is a twisted CY algebra.

Related

• The Calabi-Yau property of Hopf algebras and braided Hopf algebras
• Cleft extensions of Koszul twisted Calabi-Yau algebras
• Derived categories and Calabi-Yau algebras
• Cocommutative Calabi-Yau Hopf algebras and deformations
• Hopf-Galois objects of Calabi-Yau Hopf algebras