Braided Hopf algebras obtained from coquasitriangular Hopf algebras

\In this paper, we study the generalized quantum double construction for paired Hopf algebras with particular attention to the case when the generalized quantum double is a Hopf algebra with projection. Applying our theory to a coquasitriangular Hopf algebra (H, sigma), we see that H has an associated structure of braided Hopf algebra in the category of Yetter-Drinfeld modules over H-sigma(cop), where H-sigma is a subHopf algebra of H-0, the finite dual of H. Specializing to the quantum group H = SLq (N), we find that H-sigma is U-q(ext) (sl(N)), so that the duality between these quantum groups is just the evaluation map. Furthermore, we obtain explicit formulas for the braided Hopf algebra structure of SLq (N) in the category of left Yetter-Drinfeld modules over U-q(ext) (sl(N))(cop).