The Structure Of Hom-Dimodule And Hom-Yetter-Drinfeld Module

In this paper, we mainly discuss the following questions:one is the structure of Hom-dimodule, and Hom-dimodule algebras, Hom-dimodule coalgebras; the other is the Hom-Yetter-Drinfeld module.The dissertation is orgenized as follows:In chapter one, we introduce the background of Hopf algebras and present some con-cepts and introduce how the question investigated in this disseriation is produced.In chapter two, we introduce the conceptions of Hom-Long Equation and Hom-dimodule, and construct the solutions for Hom-Long Equation over Hom-dimodule.In chapter three, we give the Hom-dimodule algebras structures, and obtain the nec-essary and sufficient condition of the Hom-smash product of two Hom-dimodule alegbras with a weak unit and a weak counit to be a Hom-dimodule algebras. Then we give the dual result.In chapter four, we introduce the conception of Hom-Yetter-Drinfeld module firstly, and contruct the solutions for Horn-Yang-Baxter Equations on it. Then, we construct Hom-Drinfeld paired D(H), and prove the most main theorem:Hom-Yetter-Drinfeld mod-ules are equivalent to the left D(H)-Hom-modlue.