On representation of quasi-Hopf group coalgebras

Abstract

Abstract In this paper, we give the definitions of crossed quasi-Hopf π-coalgebra H and a crossed left π-H-modules, and show that the category of crossed left π-H-modules is a monoidal category. Finally, we show that a family R = {R α, β ∈ H α ⊗ H β } of elements is a quasitriangular structure of a crossed quasi-Hopf π-coalgebra H if and only if the category of crossed left π-H-modules over H is a braided monoidal category with braiding defined by R.