Maschke Theorem Over Monoidal Hom-Hopf Algebras And Fundamental Theorem Over The Hom-Yetter-Drinfeld Hopf Algebras

This paper mainly gives the Maschke theorem for twisted Hom-smash products,L-R Hom-smash products and the fundamental theorem over the Hom-Yetter-Drinfeld Hopf algebras.The whole paper consists of four chapters.In chapter 1,we introduce the recent development of Hopf algebras,the research background,the contents we studied and the main results of this paper.In chapter 2,we introduce the concept of the twisted Hom-smash products and give a necessary and sufficient condition for twisted Hom-smash products to be Hom-bialgebras(Hom-Hopf algebras),and then give the Maschke theorem for the twisted Hom-smash products.In chapter 3,we introduce the concept of the L-R Hom-smash products and give a necessary and sufficient condition for L-R Hom-smash products to be Hom-bialgebras(Hom-Hopf algebras),and then give the Maschke theorem for the L-.R Hom-smash products.In chapter 4,we give the fundamental theorem of Hom-Hopf module over the Hom-Yetter-Drinfeld Hopf algebras.