文献类型：期刊文献

英文题名：Symmetric pairs and pseudosymmetry of Theta-Yetter-Drinfeld categories for Hom-Hopf algebras

作者：Liu, Wei[2];Fang, Xiaoli[1]

机构：[1]Shaoxing Univ, Dept Math, Chengnan Ave 900, Shaoxing 312000, Zhejiang, Peoples R China;[2]Shaoxing Univ, Yuanpei Coll, Dept Math, Qunxian Middle Rd 2799, Shaoxing 312000, Zhejiang, Peoples R China

年份：2021

卷号：19

期号：1

起止页码：1231

外文期刊名：OPEN MATHEMATICS

收录：SCI-EXPANDED(收录号：WOS:000728462800001)、、Scopus(收录号：2-s2.0-85121793535)、WOS

基金：The first author was financially supported by The Research Project of Shaoxing University (No. 2020LG1009) and Research Project of Shaoxing University Yuanpei College (No. KY2020C01) . The second author was financially supported by the Natural Science Foundation of Zhejiang Province (No. LY14A010006) and the National Natural Science Foundation of China (No. 11571239) .

语种：英文

外文关键词：Hom-Hopf algebra; Theta-Yetter-Drinfeld module; symmetric pair

外文摘要：In this paper, we investigate a more general category of Theta-Yetter-Drinfeld modules (Theta is an element of Aut H (H)) over a Hom-Hopf algebra, which unifies two different definitions of Hom-Yetter-Drinfeld category introduced by Makhlouf and Panaite, Li and Ma, respectively. We show that the category of Theta-Yetter-Drinfeld modules with a bijective antipode S is a braided tensor category and some solutions of the Hom-Yang-Baxter equation and the Yang-Baxter equation can be constructed by this category. Also by the method of symmetric pairs, we prove that if a Theta-Yetter-Drinfeld category over a Hom-Hopf algebra H is symmetric, then H is trivial. Finally, we find a sufficient and necessary condition for a Theta-Yetter-Drinfeld category to be pseudosymmetric.