On topologies on Malcev completions of braid groups

We discuss groups corresponding to Kohno Lie algebra of infinitesimal braids and actions of such groups. We construct homomorphisms of Lie braid groups to the group of symplectomorphisms of the space of point configurations in $\mathbb{R}^3$ and to groups of symplectomorphisms of coadjoint orbits of $\mathrm{SU}(n)$.