Hom-quasi-bialgebras
Mohamed Elhamdadi, Abdenacer Makhlouf

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons
