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, σ), we see that H has an associated structure of braided Hopf algebra in the category of Yetter-Drinfeld modules over , where H _σ is a subHopf algebra of H ⁰, the finite dual of H. Specializing to the quantum group H = SL _q (N), we find that H _σ is , 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 SL _q (N) in the category of left Yetter-Drinfeld modules over . The second author held a postdoctoral fellowship at Mount Allison University from 2005 to 2007 and would like to thank Mount Allison for their warm hospitality. Support for the first author’s research and partial support for the postdoctoral position of the second author came from an NSERC Discovery Grant. The second author now holds research support from Grant 434/1.10.2007 of CNCSIS.