Braids of formal Poisson groups with a quasitriangular dual

Drinfeld (Proceedings of the International Congress of Mathematics (Berkley , 1986), 1987, pp. 798-820) 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 (Uh,R) is any quasitriangular QUEA, the n (U-h' ,Ad(R)/(Uh ' circle times Uh ')) is a braided QFSHA. As a consequen ce, we prove that if g is a quasitriangular Lie bialgebra over a field k of characteristic zero and g* is its dual Lie bialgebra, the algebra of funct ions 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 quantiza tion (U-h,R) of U(g) and of the fact that U-h' is a quantization of F[g*]. (C) 2001 Elsevier Science B.V. All rights reserved.