QUANTUM GROUPS AND QUANTUM SHUFFLES

Let U-q(+) be the ''upper triangular part'' of the quantized envelopin g algebra associated with a symetrizable Cartan matrix. We show that U -q(+) is isomorphic las a Hopf algebra) to the subalgebra generated by elements of degree 0 and 1 of the cotensor Hopf algebra associated wi th a suitable Hopf bimodule on the group algebra of Z(n). This method gives supersymetric as well as multiparametric versions of U-q(+) in a uniform way (for a suitable choice of the Hopf bimodule). We give a c lassification result about the Hopf algebras which can be obtained in this way, under a reasonable growth condition. We also show how the ge neral formalism allows to reconstruct higher rank quantized enveloping algebras from U(q)sl(2) and a suitable irreducible finite dimensional representation.