The Maschke-type Theorem And Morita Context Of Hom-twisted Smash Product

Let(H,?H)be a Hom-Hopf algebra and(A,?A)be an(H,?H)-Hom-bimodule Hom-algebra with ?H,?A bijective maps.Then in this paper,we first define the Hom-twisted smash product algebra(AH,?A(?)?H)and study some of its properties.Next we find some conditions for the Hom-twisted smash product to be a Hom-bialgebra and a Hom-Hopf algebra.Finally,we give a Maschke-type theorem over a semisimple Hom-Hopf algebra(H,?H)and form an associated Morita context[AbiH,AbiH)AAH,AHAAbiH,AH]between AbiH and AH.