Doubles of quasitriangular hopf algebras

Abstract

Let H be a finite dimensional Hopf algebra and D(H) the associated ”quantum double” quasitriangular Hopf algebra of Drin-feld. Previously we showed that as an example of a double cross product of Hopf algebras H H ∗op acting on each other. We now show that if H is itself quasitriangular then D(H) is a semidirect"biproduct"in the sense of Radford: There is an algebra and coalgebra B such that as an ordinary smash product and smash co-product by H. The result arises naturally in the context of representation theoretic considerations for double cross products.