拟Hopf代数上BHQ何时是预辫子monoidal范畴  

When is BHQ a pre-braided category over quasi-Hopf algebras

作　　者：郭双建[1] 李怡铮[1] GUO Shuang-jian;LI Yi-zheng;School of Mathematics and Statistics;Guizhou University of Finance and Economics;

机构地区：[1]贵州财经大学数学统计学院,贵州贵阳550025

出　　处：《山东大学学报（理学版）》2017年第12期10-15,24,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11371088);贵州省科技厅基金项目(J[2014]2045;[2016]1021);贵州省高校优秀科技创新人才支持计划(黔教合KY字[2015]481)

摘　　要：设H为带有可逆对极的拟Hopf代数,B为左拟Yetter-Drinfeld模代数,并且HBQ为拟Hopf Yetter-Drinfeld(H,B)-模范畴。讨论了范畴HBQ何时是预辫子monoidal范畴。假设B是H交换的,则拟Hopf Yetter-Drinfeld模范畴HQ上的辫子诱导出HBQ上的预辫子当且仅当HBQ中的每一个对象是dyslectic。Let H be a quasi-Hopf algebra with invertible antipode,B a left quasi Yetter-Drinfeld module algebra and ^HB Q the category of quasi Hopf Yetter-Drinfeld（H,B）-modules. It is discussed when the category ^HBQ is a pre-braided monoidal category. The following is proved： assume that B is H-commutative,then the braiding on the category of quasi Yetter-Drinfeld modules ^HQ induces a pre-braiding on ^HB Q if and only if every object of ^HBQ is dyslectic.

关 键 词：辫子monoidal范畴 拟三角拟Hopf代数 拟Yetter-Drinfeld模代数 SMASH积 

分 类 号：O153.3[理学—数学]