Representations and categorical realization of Hom-quasi-Hopf algebras

Abstract

We give a monoidal category approach to Hom-coassociative coalgebra by imposing the Hom-coassociative law up to some isomorphisms on the comultiplication map and requiring that these isomorphisms satisfy the copentagon axiom and obtain a Hom-coassociative 2-coalgebra, which is a 2- category. Second, we characterize Hom-bialgebras in terms of their categories of modules. Finally, we give a categorical realization of Hom-quasi-Hopf algebras using Hom-coassociative 2-coalgebra.

Keywords

Monoidal category / Hom-coassociative 2-coalgebra / Hom-quasi-Hopf algebra

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Higher Education Press and Springer-Verlag Berlin Heidelberg