Hopf群余代数上对角交叉积的Maschke型定理  

The Maschke-type theorems of diagonal crossed products over Hopf group coalgebras

作　　者：罗晓芳[1] 张颖颖[2] 陈笑缘[2] LOU Xiaofang;ZHANG Yinyin;CHEN Xiaoyuan(Yiwu Industrial&Commercial College,Yiwu 322000,Zhejiang Province,China;Zhejiang Business College,Hangzhou 310053,China)

机构地区：[1]义乌工商职业技术学院,浙江金华322000 [2]浙江商业职业技术学院,浙江杭州310053

出　　处：《浙江大学学报（理学版）》2023年第1期16-19,共4页Journal of Zhejiang University（Science Edition）

摘　　要：构造了Hopf群余代数上对角交叉积代数结构,给出了其为Hopf群余代数的充要条件,证明了其表示范畴同构于Yetter-Drinfeld群模范畴,并将Hopf代数理论中经典的Maschke型定理推广至Hopf群余代数的对角交叉积。In this paper, a diagonal crossed product over a Hopf group coalgebra is constructed, and the sufficient and necessary conditions for it being a Hopf group coalgebra are given. Then we prove that the representation category of a diagonal crossed product over a Hopf group coalgebra is isomorphic to the category of Yetter-Drinfeld π-modules and extend the classic Maschke-type theorem of Hopf algebra to diagonal crossed products over Hopf group coalgebras.

关 键 词：HOPF群余代数 对角交叉积 MASCHKE型定理 

分 类 号：O153.3[理学—数学]