[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]

Copy

Making the category of entwined modulesinto a braided monoidal category()

Share：

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:

[1] Brzezinski T, Majid S.Coalgebra bundles [J].Comm Math Phys, 1998, 191(2):467-492.
[2] Caenepeel S, Militaru G, Zhu S L.Doi-Hopf modules, Yetter-Drinfeld modules and Frobenius type properties [J].Trans Amer Math Soc, 1997, 349:4311-4342.
[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.
[4] Doi Y.Unifying Hopf modules [J].J Algebra, 1992, 153(2):373-385.
[5] Koppinen M.Variations on the smash product with applications to group-graded rings [J].J Pure Appl Algebra, 1995, 104(1):61-80.
[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.

Common functions