[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()

线性范畴交叉积等价及广义Maschke定理

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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

线性范畴交叉积等价及广义Maschke定理

Author(s):

Lu Daowei;  Wang Shuanhong

Department of Mathematics, Southeast University, Nanjing 211189, China

鹿道伟;  王栓宏

东南大学数学系, 南京211189

Keywords:

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

线性范畴;  内作用;  交叉积;  广义Maschke定理

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.

给出了Hopf代数与线性范畴2个不同交叉积之间等价的充要条件, 并推广了Maschke定理.基于经典Hopf代数的方法, 首先设A为k-线性范畴且H为Hopf代数, 则2个交叉积A#_σHσH与A#′_σ′H在某些条件下是同构的.其次设A#_σHσH为有限维半单Hopf代数H的交叉积范畴.若V为左A#_σHσH-模且W⊆V为V的子模, W作为左A-模在V中有补, 则W作为左A#_σHσH-模在V中有补.

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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