Tressages des groupes de Poisson formels à dual quasitriangulaire

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) Uh. In this paper, we prove that if (Uh,R) is any quasitriangular QUEA, then (U′h,Ad(R)U′hcircle times operatorU′h) is a braided QFSHA. As a consequence, we prove that if image is a quasitriangular Lie bialgebra over a field k of characteristic zero and image is its dual Lie bialgebra, the algebra of functions image on the formal group associated to image is a braided Hopf algebra. This result is a consequence of the existence of a quasitriangular quantization (Uh,R) of image and of the fact that U′h is a quantization of image.