Quasitriangular Quasi-Hopf Algebras

Abstract

By using categorical tools, we introduce the concept of quasitriangular (QT) quasi-bialgebras. For QT quasi-Hopf algebras we show that the square of the antipode is an inner automorphism, and therefore bijective. We uncover the QT structure of the quantum double D ( H ) of a finite-dimensional quasi-Hopf algebra H , and characterize D ( H ) as a biproduct quasi-Hopf algebra in the case when H itself is QT.