拟Hopf代数上BHQ何时是预辫子monoidal范畴

doi:10.6040/j.issn.1671-9352.0.2017.177

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (12): 10-15.doi: 10.6040/j.issn.1671-9352.0.2017.177

拟Hopf代数上^B_HQ何时是预辫子monoidal范畴

郭双建,李怡铮

贵州财经大学数学统计学院, 贵州贵阳 550025

收稿日期:2017-04-20 出版日期:2017-12-20 发布日期:2017-12-22
作者简介:郭双建(1981— ), 男, 博士, 副教授, 主要从事Hopf代数方面的研究. E-mail:shuangjianguo@126.com
基金资助:
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)

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

GUO Shuang-jian, LI Yi-zheng

School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China

Received:2017-04-20 Online:2017-12-20 Published:2017-12-22

摘要/Abstract

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^H_BQ为拟Hopf Yetter-Drinfeld(H,B)-模范畴。讨论了范畴^H_BQ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^H_BQ上的预辫子当且仅当^H_BQ中的每一个对象是dyslectic。

关键词: 辫子monoidal范畴, 拟Yetter-Drinfeld模代数, 拟三角拟Hopf代数, smash积

Abstract: Let H be a quasi-Hopf algebra with invertible antipode, B a left quasi Yetter-Drinfeld module algebra and ^H_BQ the category of quasi Hopf Yetter-Drinfeld (H,B)-modules. It is discussed when the category ^H_BQ 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 ^H_BQ if and only if every object of H_BQ is dyslectic.

Key words: braided monoidal category, smash product, quasitriangular quasi-Hopf algebra, quasi Yetter-Drinfeld module algebra

中图分类号:

O153.3

郭双建,李怡铮. 拟Hopf代数上^B_HQ何时是预辫子monoidal范畴[J]. 山东大学学报（理学版）, 2017, 52(12): 10-15.

GUO Shuang-jian, LI Yi-zheng. When is B_HQ a pre-braided category over quasi-Hopf algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 10-15.

参考文献

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拟Hopf代数上^B_HQ何时是预辫子monoidal范畴

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

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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

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拟Hopf代数上^B_HQ何时是预辫子monoidal范畴

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