Braiding structures on formal Poisson groups and classical solutions of the QYBE

If g is a quasitriangular Lie bialgebra, the formal Poisson group F[[g^*]] can be given a braiding structure. This was achieved by Weinstein and Xu using purely geometrical means, and independently by the authors by means of quantum groups. In this paper we compare these two approaches. First, we show that the braidings they produce share several similar properties (in particular, the construction is functorial); secondly, in the simplest case (G = SL_2) they do coincide. The question then rises of whether they are always the same this is positively answered in a separate paper.