Generalized Ore Extensions Of Hopf Group Coalgebras And The （D,H）-Hopf Modules In YD_Bα^C

In this paper, We mainly considered the necessary and sufficient conditions for the generalized Ore extensions of Hopf group coalgebras to become the Hopf group coalgebras and the fundamental theorem of (D, H)-Hopf modules in yDCBαThis paper is mainly consists of three chapters:In the first chapter, we give the research background some main results.In the second chapter, firstly we define the generalized Ore extensions of Hopf group coalgebras, and then generalize the Ore extensions of Hopf algebras to Hopf group coal-gebras. Finally we obtain the necessary and sufficient conditions for the generalized Ore extensions of Hopf group coalgebras to become the Hopf group coalgebras.In the last chapter, I.Heckenberger defined the relative Yetter-Drinfeld modules cat-egories, in this foundation, we give the special Yetter-Drinfeld modules categorie yDCBα, and introduce the Hopf algebras, module coalgebras, (D,H)-Hopf modules over cate-gories yDCBα, which is induced by relative Yetter-Drinfeld categories yDCBαAt last, We give some properties of (D,H)-Hopf modules and the isomorphism theorems in yDCBα...