  In this paper we mainly construct bicrossproduct for finite-dimensional
monoidal Hom-Hopf algebra $(H,\alpha)$, generalizing the Majid's
bicrossproduct. Naturally the Hom-type bicrossproduct leads to Drinfel'd double
$(H^{op}\bowtie H^{\ast}, \alpha \otimes (\alpha^{-1})^\ast)$ with a
quasitriangular structure $R$ satisfying the quantum Hom-Yang-Baxter equations.

Rings and Algebras