Doi Hom-Hopf模的Maschke型定理  

Maschke Type Theorem for Doi Hom-Hopf Modules

作　　者：郑玛丽[1] 

机构地区：[1]蚌埠学院数学与物理系,安徽蚌埠233030

出　　处：《吉林大学学报（理学版）》2016年第2期202-206,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金天元基金(批准号:11426073);贵州省科学技术基金(批准号:2014GZ81365)

摘　　要：考虑Doi Hom-Hopf模的半单性或可约性.设(H,A,C)是一个Doi Hom-Hopf-数据,先利用忘却函子将Doi Hom-Hopf模范畴MCA中的对象映为右(A,β)-Hom模范畴MA中对象,再通过对MA中可分单同态进行变形,建立Doi Hom-Hopf-数据积分概念,并利用该积分证明Doi Hom-Hopf模的Maschke型定理.作为应用,定义了Hom-Yetter-Drinfeld模范畴,并证明HomYetter-Drinfeld模范畴是Doi Hom-Hopf模范畴的子范畴,从而得到了Hom-Yetter-Drinfeld模的Maschke型定理.The author discussed the reducibility or semisimpleness of Doi Hom-Hopf modules. Given a Doi Hom-Hopf datum（ H,A,C）,the forgetful functor was used to send the objects in the category MCAof Doi HomHopf modules into the category MAof right（ A,β）-Hom-modules,and look for a deformation of a splitting map of a monomorphism in the category MAso as to lead to the integral for Doi Hom-Hopf datum（ H,A,C）. With the help of the integral introduced,the author proved the Maschke-type theorem for Doi Hom-Hopf modules.As an application,the author defined the category of Hom-Yetter-Drinfeld modules and proved the category of Hom-Yetter-Drinfeld modules being a subcategory of our category of Doi Hom-Hopf modules,then the author obtained immediately the version of Maschke type theorem for Hom-Yetter-Drinfeld modules.

关 键 词：Monoidal Hom-Hopf代数 DOI Hom-Hopf模 MASCHKE型定理 Hom-Yetter-Drinfeld模 

分 类 号：O153.3[理学—数学]