中文摘要：

Let(C, α) and(H, β) be Hom-bialgebras and ω : C H→ H C a linear map. We introduce a Hom-ω-smash coproduct(Cω■H, γ) and give necessary and sufficient conditions for(Cω■H, γ) to be a Hom-bialgebra. We study the quasi-triangular structures over(Cω■H, γ)and show the necessary and sufficient conditions for(Cω■H, γ, R) to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D(H)*and construct quasi-triangular structures over D(H)*.

英文摘要：

Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be a Hom-bialgebra. We study the quasi-triangular structures over （Cω H, γ） and show the necessary and sufficient conditions for （Cω H, γ R） to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D（H）＊ and construct quasi-triangular structures over D（H）＊.