[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()

构造entwined模范畴成为辫子张量范畴

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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

构造entwined模范畴成为辫子张量范畴

Author(s):

Liu Ling;  Wang Shuanhong

Department of Mathematics, Southeast University, Nanjing 211189, China

刘玲;  王栓宏

东南大学数学系, 南京 211189

Keywords:

Doi-Hopf module;  entwined module;  braided monoidal category

Doi-Hopf模;  entwined模;  辫子张量范畴

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.

研究了如何使entwined模范畴成为辫子张量范畴.首先, 利用如果(A, C, ψ)是一个entwining结构, 那么A⊗C形成entwined模的结论可以得到entwined模范畴成为张量范畴的充要条件.条件是要求问题中的代数和余代数都必须为双代数而且满足某些相容条件.然后, 在给定的张量entwined模范畴上, 通过一个扭曲卷积可逆映射Q定义了辫子, 并且由类似的方法得到使entwined模范畴构成辫子张量范畴的充分必要条件.最后, 作为示例将得到的结果应用到Doi-Hopf模和(α, β)-Yetter-Drinfeld 模范畴中.

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.

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