Tressages des groupes de Poisson formels à dual quasitriangulaire

AbstractDrinfeld (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′h⊗U′h) 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, 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 (Uh,R) of U(g) and of the fact that U′h is a quantization of F〚g∗〛