The logarithmic star product in the linear case and the Grothendieck--Teichmüller group

Abstract

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-Teichmüller group.

arXiv commentThe paper has been withdrawn, because I have posted it wrongly the first time on the arXiv. Then, I decided to change the title radically and added some more technical details