DOUBLES OF QUASI-TRAINGULAR HOPF-ALGEBRAS

Let H be a finite dimensional Hopf algebra and D(H) the associated "quantum double" quasitriangular Hopf algebra of Drinfeld. Previously we showed that D(H) congruent-to H H*op 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 D(H) congruent-to H X B 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.