The explicit equivalence between the standard and the logarithmic star product for Lie algebras, I

Abstract

The purpose of this note is to establish an explicit equivalence between two star products ⋆ and ⋆log on the symmetric algebra S(g) of a finite-dimensional Lie algebra g over a field K⊃C associated with the standard angular propagator and the logarithmic one respectively: the differential operator of infinite order with constant coefficients realizing the equivalence is related to the incarnation of the Grothendieck–Teichmüller group considered by Kontsevich (1999) in [5, Theorem 7]. We present in the first part the main result, and devote the second part to its proof.