A NATURAL AND RIGID MODEL OF QUANTUM GROUPS

We introduce a natural (Frechet-Hopf) algebra A containing all generic Jimbo algebras U(t)(sl(2)) (as dense subalgebras). The Hopf structures on A extend (in a continuous way) the Hopf structures of generic U(t)(sl(2)). The Universal R-matrices converge in A x A. Using the (topological) dual of A, we recover the formalism of functions of noncommutative arguments. In addition, we show that all these Hopf structures on A are isomorphic (as bialgebras), and rigid in the category of bialgebras.