Tressages des groupe de Poisson formels \`a dual quasitriangulaire

Let $\mathfrak{g}$ be a quasitriangular Lie bialgebra over a field $K$ of characteristic zero, and let $\mathfrak{g}^*$ be its dual Lie bialgebra. We prove that the formal Poisson group $K\big[\big[\mathfrak{g}^*\big]\big]$ is a braided Hopf algebra, thus generalizing a result due to Reshetikhin (in the case $\, \mathfrak{g} = \mathfrak{sl}(2,K) \,$). The proof is via quantum groups, using the existence of a quasitriangular quantization of $\mathfrak{g}^*$, as well as the fact that this one provides also a quantization of $K\big[\big[\mathfrak{g}^*\big]\big] \,$.