THE HOM-TWISTED SMASH PRODUCT BIALGEBRAS

Let (H, alpha(H)) be a Hom-Hopf algebra and (A, alpha(A)) be an (H, alpha(H))-Hom-bimodule algebra with the maps alpha(A), alpha(H) bijective. Then in this paper, we first introduce the notion of Hom-twisted smash product (A* H, alpha(A) * alpha(H)) and then study the conditions for the Hom-twisted smash product and tensor coproduct to form a Hom-bialgebra and a Hom-Hopf algebra. Furthermore, we give a non-trival example of Hom-twisted smash product Hopf algebra and a characterization of left (A * H, alpha(A) * alpha(H))-Hom module.