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

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
[1] DRINFELD V G. Quasi-Hopf algebras[J]. Leningrad Math J, 1990, 1:1419-1457.
[2] DRINFELD V G. Quasi-Hopf algebras and Knizhnik-Zamolodchikov equations[M] // Problems of Modern Quantum Field Theory. Berlin: Springer,1989: 1-13
[3] BULACU D, PANAITE F, VAN OYSTAEYEN F. Quasi-Hopf algebra actions and smash product[J]. Comm Algebra, 2000, 28:631-651.
[4] WANG Shuanhong. Braided monoidal categories associated Yetter-Drinfeld categories[J]. Comm Algebra, 2002, 30:5111-5124.
[5] BULACU D, NAUWELAERTS E. Radfords biproduct for quasi-Hopf algebras and bosonization[J]. J Pure Appl Algebra, 2002, 174:1-42.
[6] BULACU D, PANAITE F, CAENEPEEL S. Yetter-Drinfeld categories for quasi-Hopf algebra[J]. Comm Algebra, 2006, 34:1-35.
[7] PAREIGIS B. On braiding and dyslexia[J]. J Algebra, 1995, 171(2):413-425.
[8] CAENEPEEL S, VAN OYSTAEYEN F, ZHANG Yinhuo. Quantum Yang-Baxter module algebras[J]. K-theory, 1994, 8(3):231-255.
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