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.
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)
