设(H,α)是monoidal Hom-Hopf代数,(B,β)是左H,α)-Hom-余模余代数.构造了由Hom-扭曲积Bσ[H]Hom-余代数。构成的新monoidal Horn-Bx^#H.并给出了Bx^#H 成为monoidal Horn-双代数的充分必要条件此外,设(H,α)是带有Hom-σr-反对极SH的Hom-σ-Hopf代数,并找到此monoidalHorn-双代数Bx^3带有定义为S(b×h)=(1B×SH(a^-1)b(-1)))(SB(b(0))×1H的反对极S成为monoidalHom-Hopf代数的充分条件.
Let (H, a) be a monoidal Hom-bialgebra and (B,p) be a left (H, a)-Hom-comodule coalgebra. The new monoidal Hom-algebra B#y H is constructed with a Hom-twisted product Ba[H] and a. B × H Hom-smash coproduct. Moreover, a sufficient and necessary condition for B#y / to be a monoidal Hom-bialgebra is given. In addition, let (H, a) be a Hom-σ- Hopf algebra with Hom-〇 --antipode SH, and a sufficient condition for this new monoidal Hom-bialgebra B#y H with the antipode S defined by S(b×h)=(1B×SH(a^-1)b(-1)))(SB(b(0))×1H to be a monoidal Hom-Hopf algebra is derived.