[Compatibilité entre cup-produits, connexion dʼAlekseev–Torossian et conjecture de Kashiwara–Vergne, II]
On donne ici une preuve différente de la compatibilité entre cup produits (Kontsevich, 2003, [3, Section 8]) en cohomologie de degré 0 dans le cas dʼune algèbre de Lie de dimension finie, dʼoù on déduit, en utilisant la connection de Alekseev–Torossian (Alekseev et Torossian, 2010, [1]), une écriture alternative du produit-étoilé de Kontsevich.
We give a different proof of the famous result on compatibility between cup product (Kontsevich, 2003, [3, Section 8]) in cohomology of degree 0, for a finite-dimensional Lie algebra, from which we deduce an alternative way of re-writing Kontsevichʼs star product by means of the Alekseev–Torossian connection (Alekseev and Torossian, 2010, [1]).
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@article{CRMATH_2012__350_19-20_871_0,
author = {Rossi, Carlo A.},
title = {On the compatibility between cup products, the {Alekseev{\textendash}Torossian} connection and the {Kashiwara{\textendash}Vergne} conjecture, {II}},
journal = {Comptes Rendus. Math\'ematique},
pages = {871--874},
publisher = {Elsevier},
volume = {350},
number = {19-20},
year = {2012},
doi = {10.1016/j.crma.2012.09.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.09.017/}
}
TY - JOUR AU - Rossi, Carlo A. TI - On the compatibility between cup products, the Alekseev–Torossian connection and the Kashiwara–Vergne conjecture, II JO - Comptes Rendus. Mathématique PY - 2012 SP - 871 EP - 874 VL - 350 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.09.017/ DO - 10.1016/j.crma.2012.09.017 LA - en ID - CRMATH_2012__350_19-20_871_0 ER -
%0 Journal Article %A Rossi, Carlo A. %T On the compatibility between cup products, the Alekseev–Torossian connection and the Kashiwara–Vergne conjecture, II %J Comptes Rendus. Mathématique %D 2012 %P 871-874 %V 350 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.09.017/ %R 10.1016/j.crma.2012.09.017 %G en %F CRMATH_2012__350_19-20_871_0
Rossi, Carlo A. On the compatibility between cup products, the Alekseev–Torossian connection and the Kashiwara–Vergne conjecture, II. Comptes Rendus. Mathématique, Tome 350 (2012) no. 19-20, pp. 871-874. doi : 10.1016/j.crma.2012.09.017. http://www.numdam.org/articles/10.1016/j.crma.2012.09.017/
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