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Hom-quasi-bialgebras

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.