A generalized double crossproduct for monoidal Hom-Hopf algebras and the Drinfeld double
Volume 146 / 2017
Colloquium Mathematicum 146 (2017), 213-238
MSC: Primary 16W30; Secondary 18B40.
DOI: 10.4064/cm6633-3-2016
Published online: 3 October 2016
Abstract
A twisted generalization of a double crossproduct called a generalized double Hom-crossproduct is introduced. We give conditions under which this new monoidal Hom-algebra is a monoidal Hom-Hopf algebra. Moreover, its coquasitriangular structure is described. Finally, we also construct a new braided monoidal Hom-category $\widetilde{\mathcal{H}}(_{J}^{J}\operatorname{Mod}^Q_Q)$ obtained from the structure of the generalized double Hom-crossproduct, and establish a kind of new quantum Yang–Baxter Hom-operators.
