JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (8): 107-110.doi: 10.6040/j.issn.1671-9352.0.2016.582

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The fundamental theorem forAMHH in Yetter-Drinfeld module categories

CHEN Hua-xi1, XU Qing-bing2   

  1. 1. Department of Mathematics and Physics, Bengbu College, Bengbu 233000, Anhui, China;
    2. Department of Basic course, Chuzhou Vocational and Technical Colege, Chuzhou 239000, Anhui, China
  • Received:2016-12-15 Online:2017-08-20 Published:2017-08-03

Abstract: The definitions of weak Hopf algebra and weak comodule algebras in Yetter-Drinfeld module categories are introduced, and the fundamental theorem forAMHH in Yetter-Drinfeld module categories is obtained.

Key words: weak comodule algebra, Yetter-Drinfeld module category, weak Hopf algebra

CLC Number: 

  • O153.3
[1] BÖHM G, NILL F, SZLACHÁNYI K. Weak Hopf algebras: Ⅰ. integral theory and C*-structure[J]. J Algebra,1999, 221(2):385-438.
[2] ZHANG L Y. ZHU S L. Fundamental theorems of weak Doi—Hopf modules and semisimple weak smash product Hopf algebras[J]. Comm Algebra, 2004, 32(9):3403-3415.
[3] CAENEPEEL S, WANG D G, YIN Y M. Yetter-Drinfeld modules over weak Hopf algebras[J]. Ann Univ Ferrara, 2005, 51(1):69-98.
[4] DOI Y. Hopf modules in Yetter-Drinfeld category[J]. Comm Algebra, 1998, 26(9): 3057-3070.
[5] MONTGOMERY S. Hopf algebras and their actions on rings[M]. Providence, Rhode Island: Amer Math Soc, 1993.
[6] HAYASHI T. Quantum group symmetry of partition functions of IRF models and its applications to Joness index theory[J]. Comm Math Phys, 1993, 157:331-345.
[7] NIKSHYCH D, Vainerman L. Finite quantum groupoids and their applications[J]. Math Sci Res Inst Publ, 2002, 43:211-262.
[8] NIKSHYCH D. A duality theorem for quantum groupoids[J]. Contemp Math, 2000, 267:237-243.
[9] YAMANOUCHI T. Duality for generalized Kac algebras and a characteriztion of finite groupoid algebras[J]. J Algebra, 1994, 163:9-50.
[1] DONG Li-hong1,2, GUO Shuang-jian1. The fundamental theorem for weak Hopf module in  Yetter-Drinfeld module categories [J]. J4, 2013, 48(2): 20-22.
[2] CHEN Hua-xi1, ZHANG Xiao-hui2, XU Qing-bing3. The Structure Theorem of weak comodule algebras in
Yetter-Drinfeld module categories
[J]. J4, 2013, 48(12): 14-17.
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