Doi-Hopf Modules Over Hom-Hopf Algebras

This paper mainly studies the Doi Hom-Hopf modules over Hom-Hopf algebras Firstly,we introduce the forgetful functor F:M(H)AC?MA and prove that F has a right adjoint G:MA?M(H)AC on the Hom-Hopf algebra(H,?);Secondly,the necessary and sufficient conditions for forgetful functor F to be separable functor are introduced by constructing a normalized integral ?.Moreover,we introduce the definition of the category Hom-Yetter-Drinfeld modules over Hom-Hopf algebra,and prove that it is isomorphic to the category of special Doi Hom-Hopf modules;Finally,we give the tensor identities for the category of Doi Hom-Hopf modules.