Drinfel’d double for monoidal Hom-Hopf algebras
Volume 164 / 2021
Colloquium Mathematicum 164 (2021), 251-271
MSC: Primary 16T05.
DOI: 10.4064/cm8076-1-2020
Published online: 23 September 2020
Abstract
We mainly construct a bicrossproduct for a finite-dimensional monoidal Hom-Hopf algebra $(H,\alpha )$, generalizing Majid’s bicrossproduct. Naturally, the Hom-type bicrossproduct leads to the Drinfel’d double $(H^{\rm op}\bowtie H^{\ast },\alpha \otimes (\alpha ^{-1})^{\ast })$ with a quasitriangular structure $R$ satisfying the quantum Hom-Yang–Baxter equations.
