Monoidal Hom-hopf algebra on Hom-twisted product

Let (H, α) be a monoidal Hom-bialgebra and (B, β) be a left (H, α)-Hom-comodule coalgebra. The new monoidal Hom-algebra B× #H is constructed with a Hom-twisted product Bσ[H] and a B×H Hom-smash coproduct. Moreover, a sufficient and necessary condition for B× #H to be a monoidal Hom-bialgebra is given. In addition, let (H, α) be a Hom-σ-Hopf algebra with Hom-σ-antipode SH, and a sufficient condition for this new monoidal Hom-bialgebra B× #H with the antipode S defined by S(b×h)=(1B×SH(α-1(b(-1))))·(SB(b(0)>)×1H) to be a monoidal Hom-Hopf algebra is derived. © 2016, Editorial Department of Journal of Southeast University. All right reserved.