Hom-quasi-bialgebras

TL;DR

This paper surveys Hom-bialgebras, extends quasi-bialgebra concepts to the Hom-setting, and introduces key constructions, gauge transformations, and an example of a twisted quantum double.

Contribution

It introduces the concept of Hom-quasi-bialgebras, generalizes gauge transformations and Drinfeld twists to this setting, and provides an explicit example of a twisted quantum double.

Findings

Hom-bialgebras are generalized with twisted identities.

Extended quasi-bialgebra concepts to the Hom-setting.

Constructed an example of a twisted quantum double.

Abstract

The purpose of this paper is to give a general survey of Hom-bialgebras, which are bialgebra-type structures where the identities are twisted by a morphism, and to extend the concept of quasi-bialgebra to Hom-setting. We provide some key constructions and generalize the concept of gauge transformation and Drinfeld's twists to this type of generalized quasi-bialgebras. Moreover, we provide an example of twisted quantum double.