[1] Lu Daowei, Wang Shuanhong,. Equivalence of crossed product of linear categoriesand generalized Maschke theorem [J]. Journal of Southeast University (English Edition), 2016, 32 (2): 258-260. [doi:10.3969/j.issn.1003-7985.2016.02.020]

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Equivalence of crossed product of linear categoriesand generalized Maschke theorem()

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

Volumn:

32

Issue:

2016 2

Page:

258-260

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2016-06-20

Info

Title:

Equivalence of crossed product of linear categoriesand generalized Maschke theorem

Author(s):

Lu Daowei;  Wang Shuanhong

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

linear category;  inner action;  crossed product;  generalized Maschke theorem

PACS:

O153.3

DOI:

10.3969/j.issn.1003-7985.2016.02.020

Abstract:

Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σHσH and A#′_σ′H are isomorphic under some conditions. Then, let A#_σHσH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#_σHσH-module and W⊆V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σHσH-module.

References:

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Memo

Memo:

Biographies: Lu Daowei(1987—), male, graduate; Wang Shuanhong(corresponding author), male, professor, shuanhwang2002@yahoo.com.
Foundation items: The National Natural Science Foundation of China(No.11371088), the Natural Science Foundation of Jiangsu Province(No.BK2012736), the Fundamental Research Funds for the Central Universities, the Research Innovation Program for College Graduates of Jiangsu Province(No.KYLX15_0109).
Citation: Lu Daowei, Wang Shuanhong. Equivalence of crossed product of linear categories and generalized Maschke theorem[J].Journal of Southeast University(English Edition), 2016, 32(2):258-260.doi:10.3969/j.issn.1003-7985.2016.02.020.

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