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[1] Liu Ling, Wang Shuanhong,. Making the category of entwined modulesinto a braided monoidal category [J]. Journal of Southeast University (English Edition), 2008, 24 (2): 250-252. [doi:10.3969/j.issn.1003-7985.2008.02.026]
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Making the category of entwined modulesinto a braided monoidal category()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
24
Issue:
2008 2
Page:
250-252
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2008-06-03

Info

Title:
Making the category of entwined modulesinto a braided monoidal category
Author(s):
Liu Ling Wang Shuanhong
Department of Mathematics, Southeast University, Nanjing 211189, China
Keywords:
Doi-Hopf module entwined module braided monoidal category
PACS:
O153.3
DOI:
10.3969/j.issn.1003-7985.2008.02.026
Abstract:
The question of how the category of entwined modules can be made into a braided monoidal category is studied.First, the sufficient and necessary conditions making the category into a monoidal category are obtained by using the fact that if(A, C, ψ)is an entwining structure, then A⊗C can be made into an entwined module.The conditions are that the algebra and coalgebra in question are both bialgebras with some extra compatibility relations.Then given a monodial category of entwined modules, the braiding is constructed by means of a twisted convolution invertible map Q, and the conditions making the category form into a braided monoidal category are obtained similarly.Finally, the construction is applied to the category of Doi-Hopf modules and(α, β)-Yetter-Drinfeld modules as examples.

References:

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[3] Caenepeel S, van Oystaeyen F, Zhou B.Making the category of Doi-Hopf modules into a braided monoidal category [J].Algebras and Representation Theory, 1998, 1(1):75-96.
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[6] Montogomery S.Hopf algebras and their actions on rings [M].Providence, RI:American Mathematical Society, 1993.
[7] Panaite P, Staic M D.Generalized(anti)Yetter-Drinfeld modules as components of a braided T-category [J].Israel J Math, 2007, 158(1):349-366.

Memo

Memo:
Biographies: Liu Ling(1982—), female, graduate;Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang2002@yahoo.com.
Foundation items: Specialized Research Fund for the Doctoral Program of Higher Education(No.20060286006), the National Natural Science Foundation of China(No.10571026).
Citation: Liu Ling, Wang Shuanhong.Making the category of entwined modules into a braided monoidal category[J].Journal of Southeast University(English Edition), 2008, 24(2):250-252.
Last Update: 2008-06-20