JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (12): 10-15.doi: 10.6040/j.issn.1671-9352.0.2017.177

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

GUO Shuang-jian, LI Yi-zheng   

  1. 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

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Abstract: Let H be a quasi-Hopf algebra with invertible antipode, B a left quasi Yetter-Drinfeld module algebra and HBQ 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 HBQ if and only if every object of HBQ is dyslectic.

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

CLC Number: 

  • O153.3
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