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[1] Guo ShuangjianDong LihongWang Shuanhong,. Morita context of weak Hopf group coalgebras [J]. Journal of Southeast University (English Edition), 2012, 28 (3): 372-374. [doi:10.3969/j.issn.1003-7985.2012.03.021]
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Morita context of weak Hopf group coalgebras()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
28
Issue:
2012 3
Page:
372-374
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2012-09-30

Info

Title:
Morita context of weak Hopf group coalgebras
Author(s):
Guo ShuangjianDong LihongWang Shuanhong
Department of Mathematics, Southeast University, Nanjing 211189, China
Keywords:
weak Hopf π-coalgebra;  Morita context;  weak π-H-comodule algebra;  weak smash product
PACS:
O153.3
DOI:
10.3969/j.issn.1003-7985.2012.03.021
Abstract:
The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras(quantum groupoids)and Hopf group coalgebras. Let π be a group. The Morita context is considered in the sense of weak Hopf π-coalgebras. Let H be a finite type weak Hopf π-coalgebra, and A a weak right π-H-comodule algebra. It is constructed that a Morita context connects A#H* which is a weak smash product and the ring of coinvariants AcoH. This result is the generalization of that of Wang’s in the paper “Morita contexts, π-Galois extensions for Hopf π-coalgebras” in 2006. Furthermore, the result is important for constructing weak π-Galois extensions.

References:

[1] Böhm G, Nill F, Szlachányi K. Weak Hopf algebras Ⅰ: integral theory and C*-structure [J]. Journal of Algebra, 1999, 221(2):385-438.
[2] Nikshych D, Vainerman L. Finite quantum groupoids and their applications [J]. Publications of the Research Institute for Mathematical Sciences, 2002, 43(1): 211-262.
[3] Zhang L Y. Maschke-type theorem and Morita context over weak Hopf algebras[J]. Science in China: Series A, 2006, 49(5): 587-598.
[4] Turaev V. Homotopy quantum field theory[M]. European Mathematical Society, 2010.
[5] Virelizier A. Hopf group-coalgebras[J]. Journal of Pure and Applied Algebra, 2002, 171(1):75-122.
[6] Wang S H. Morita contexts, π-Galois extensions for Hopf π-coalgebras[J]. Communications in Algebra, 2006, 34(2):521-546.
[7] Van Daele A, Wang S H. New braided crossed categories and Drinfel’d quantum double for weak Hopf group coalgebras[J]. Communications in Algebra, 2008, 36(6): 2341-2386.

Memo

Memo:
Biographies: Guo Shuangjian(1981—), male, graduate; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang2002@yahoo.com.
Foundation item: The Scientific Research Innovation Project for College Graduates in Jiangsu Province(No.CXLX_0094).
Citation: Guo Shuangjian, Dong Lihong, Wang Shuanhong. Morita context of weak Hopf group coalgebras[J].Journal of Southeast University(English Edition), 2012, 28(3):372-374.[doi:10.3969/j.issn.1003-7985.2012.03.021]
Last Update: 2012-09-20