[1] Zhang Xiaohui, Wang Shuanhong,. Construction of semisimple categoryover generalized Yetter-Drinfeld modules [J]. Journal of Southeast University (English Edition), 2013, 29 (4): 467-469. [doi:10.3969/j.issn.1003-7985.2013.04.021]

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Construction of semisimple categoryover generalized Yetter-Drinfeld modules()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

29

Issue:

2013 4

Page:

467-469

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2013-12-20

Info

Title:

Construction of semisimple categoryover generalized Yetter-Drinfeld modules

Author(s):

Zhang Xiaohui;  Wang Shuanhong

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

semisimple Hopf algebra;  semisimple category;  generalized Yetter-Drinfeld module

PACS:

O153.3

DOI:

10.3969/j.issn.1003-7985.2013.04.021

Abstract:

Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD(H)is considered, where YD(H)means the disjoint union of the category of generalized Yetter-Drinfeld modules _HHYD^HH(α, β)for any α, β∈Aut_Hopf(H). First, the fact that YD(H)is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD(H)satisfies the exact condition. Thus each object in YD(H)can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD(H)is a semisimple category.

References:

[1] Panaite F, Staic M D. Generalized(anti)Yetter-Drinfeld modules as components of a braided T-category [J]. Israel J Math, 2007, 158(1): 349-365.
[2] Liu L, Wang S H. Constructing new braided T-categories over weak Hopf algebras [J]. Appl Categor Struct, 2010, 18(4): 431-459.
[3] Turaev V. Homotopy quantum field theory [M]. Bloomington: European Mathematical Society, 2010.
[4] Etingof P, Nikshych D, Ostrik V. On fusion categories [J]. Annals of Mathematics, 2005, 162(2): 581-642.
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[6] Naidu D, Rowell E. A finiteness property for braided fusion categories [J]. Algebr Represent Theor, 2011, 14(5): 837-855.
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Memo

Memo:

Biographies: Zhang Xiaohui(1985—), male, graduate; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang2002@yahoo.com.
Foundation items: The National Natural Science Foundation of China(No.11371088), the Fundamental Research Funds for the Central Universities(No.3207013906), the Natural Science Foundation of Jiangsu Province(No.BK2012736).
Citation: Zhang Xiaohui, Wang Shuanhong. Construction of semisimple category over generalized Yetter-Drinfeld modules[J].Journal of Southeast University(English Edition), 2013, 29(4):467-469.[doi:10.3969/j.issn.1003-7985.2013.04.021]

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