Tressages des groupes de Poisson formels à dual quasitriangulaire

In [V. G. Drinfeld, "Quantum groups", Proc. Intern. Congress of Math. (Berkeley, 1986) 1987, pp. 798-820], Drinfeld constructs a Quantum Formal Series Hopf Algebra (QFSHA) U'_h starting from a Quantum Universal Enveloping Algebra (QUEA) U_h . In this paper, we prove that if (U_h,R) is any quasitriangular QUEA, then U'_h with the restriction of Ad(R) to its tensor square is a braided QFSHA. As a consequence, we prove that if g is a quasitriangular Lie bialgebra over a field k of characteristic zero and g^* is its dual Lie bialgebra, then the algebra of functions F[[g^*]] on the formal group associated to g^* is a braided Hopf algebra. This result is a consequence of the existence of a quasitriangular quantization (U_h,R) of U(g) and of the fact that U'_h is a quantization of F[[g^*]] .