The Hom-comodule And Hom-Hopf Module Structure Over Hom-coalgebras

This thesis is mainly made up of three parts:In the first part:Based on the definitions of Hom-algebras, Hom-coalgebras, Hom-bialgebras, weak units, weak counits and Hom-Hopf algebras, we get some properties about antipodes. Then, we define Hom-Hopf modules, and obtain the structure theorem of Hom-Hopf modules.In the second part:Firstly, we define Hom-comodule coalgebras and get some properties about them, and study how to get Hom-comodule coalgebras by comodule coalgebras. In addition, we construct Hom-smash copruducts by Hom-comodule coal-gebras, and prove Hom-smash copruducts are Hom-coalgebras. Secondly, we difine Hom-Hopf module coalgebras and give two examples. Lastly, we give the necessary and sufficient conditions which make Hom-module coalgebras into Hom-Hopf module coalgebras.In the third part:The co-convolutions are defined in Hom(A, C), where A is a Hom-algebra and C is a Hom-coalgebra, and Hom-coalgras contained in Hom(A, C) are constructed. Further, the Hom-coalgebras constructed by the co-convolutions and Hom-algebras constructed by the convolutions become either Hom-bialgebras or Hom-Hopf algebras.