  The purpose of this short note is to establish an explicit equivalence
between two star products $\star$ and $\star_{\log}$ on the symmetric algebra
$\mathrm S(\mathfrak g)$ of a finite-dimensional Lie algebra $\mathfrak g$ over
a field $\mathbb K\supset\mathbb C$ of characteristic 0: the differential
operator of infinite order with constant coefficients realizing the equivalence
is related to the Grothendieck-Teichm\"uller group.
