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

Abstract

The purpose of this short note is to establish an explicit equivalence between the two star products \star and log\star_{\log} on the symmetric algebra S(g)\mathrm S(\mathfrak g) of a finite-dimensional Lie algebra g\mathfrak g over a field KC\mathbb K\supset\mathbb C of characteristic 0 associated with the standard angular propagator and the logarithmic one: the differential operator of infinite order with constant coefficients realizing the equivalence is related to the incarnation of the Grothendieck-Teichm\"uller group considered by Kontsevich.Comment: 2 figures; corrected and completed the formulation of Theorem 3.7. Comments are very welcome

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