Hopf Quasimodules and Yetter-Drinfeld Modules over Hopf Quasigroups

• 作者: Tao Zhang Yue Gu Shuanhong Wang
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 213-242
• 页数: 30页
• 语种: 英文
• DOI: 10.1142/S1005386721000183

摘要

We introduce the notions of a four-angle Hopf quasimodule and an adjoint quasiaction over a Hopf quasigroup H in a symmetric monoidal category C.If H possesses an adjoint quasiaction,we show that symmetric Yetter-Drinfeld categories are trivial,and hence we obtain a braided monoidal category equivalence between the category of right Yetter-Drinfeld modules over H and the category of four-angle Hopf modules over H under some suitable conditions.