[Une équivalence explicite entre les produit-étoilés standard et logarithmique pour une algèbre de Lie, I]
Dans cette note, on construit explicitement une équivalence entre les deux produits-étoilés ⋆ et sur lʼalgèbre symétrique associée à une algèbre de Lie de dimension finie sur un corps , construits en utilisant le propagateur angulaire standard et le propagateur logarithmique respectivement : lʼoperateur differentiel dʼordre infini à coéfficients constants réalisant cette équivalence est relié à lʼincarnation du groupe de Grothendieck–Teichmüller considérée par Kontsevich (1999) dans [5, Theorem 7]. On présente dans cette première partie le résultat principal, dont la démonstration sera donnée dans la deuxième partie.
The purpose of this note is to establish an explicit equivalence between two star products ⋆ and on the symmetric algebra of a finite-dimensional Lie algebra over a field 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.
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@article{CRMATH_2012__350_13-14_661_0,
author = {Rossi, Carlo A.},
title = {The explicit equivalence between the standard and the logarithmic star product for {Lie} algebras, {I}},
journal = {Comptes Rendus. Math\'ematique},
pages = {661--664},
publisher = {Elsevier},
volume = {350},
number = {13-14},
year = {2012},
doi = {10.1016/j.crma.2012.08.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.08.001/}
}
TY - JOUR AU - Rossi, Carlo A. TI - The explicit equivalence between the standard and the logarithmic star product for Lie algebras, I JO - Comptes Rendus. Mathématique PY - 2012 SP - 661 EP - 664 VL - 350 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.08.001/ DO - 10.1016/j.crma.2012.08.001 LA - en ID - CRMATH_2012__350_13-14_661_0 ER -
%0 Journal Article %A Rossi, Carlo A. %T The explicit equivalence between the standard and the logarithmic star product for Lie algebras, I %J Comptes Rendus. Mathématique %D 2012 %P 661-664 %V 350 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.08.001/ %R 10.1016/j.crma.2012.08.001 %G en %F CRMATH_2012__350_13-14_661_0
Rossi, Carlo A. The explicit equivalence between the standard and the logarithmic star product for Lie algebras, I. Comptes Rendus. Mathématique, Tome 350 (2012) no. 13-14, pp. 661-664. doi : 10.1016/j.crma.2012.08.001. http://www.numdam.org/articles/10.1016/j.crma.2012.08.001/
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