Equivalence of crossed product of linear categories and generalized Maschke theorem  

线性范畴交叉积等价及广义Maschke定理（英文）

作　　者：鹿道伟[1] 王栓宏[1] 

机构地区：[1]东南大学数学系,南京211189

出　　处：《Journal of Southeast University(English Edition)》2016年第2期258-260,共3页东南大学学报（英文版）

基　　金：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)

摘　　要：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#_σH and A#＇_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-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#_σH与A#'_(σ')H在某些条件下是同构的.其次设A#_σH为有限维半单Hopf代数H的交叉积范畴.若V为左A#_σH-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#_σH-模在V中有补.

关 键 词：linear category inner action crossed product generalized Maschke theorem 

分 类 号：O153.3[理学—数学]