Lie Algebras/Mathematical Physics
On the compatibility between cup products, the Alekseev–Torossian connection and the Kashiwara–Vergne conjecture, I
Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 823-826.

For a finite-dimensional Lie algebra g over a field KC, we deduce from the compatibility between cup products (Kontsevich, 2003, [6, Section 8]), on the one hand, and from the Kashiwara–Vergne conjecture (Kashiwara and Vergne, 1978, [4]), on the other hand, alternative ways of re-writing Kontsevich product ⋆ on S(g).

In this first part, we fix notation and conventions, revise the main features of Kontsevichʼs star product and examine the Kashiwara–Vergne conjecture and its relationship with Kontsevichʼs star product.

Soit g une algèbre de Lie de dimension finie sur un champ KC. Du résultat (Kontsevich, 2003, [6, Section 8]) sur la compatibilité entre cup produits et de la conjecture de Kashiwara–Vergne (Kashiwara et Vergne, 1978, [4]), on déduit deux écritures alternatives du produit-étoilé de Kontsevich sur S(g).

Dans cette première partie, on fixe la notation et les conventions ; on rappelle le produit-étoilé de Kontsevich, on discute la conjecture de Kashiwara–Vergne et la relation entre elle et le produit-étoilé de Kontsevich.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2012.08.002
Rossi, Carlo A. 1

1 MPIM Bonn, Vivatsgasse 7, 53111 Bonn, Germany
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Rossi, Carlo A. On the compatibility between cup products, the Alekseev–Torossian connection and the Kashiwara–Vergne conjecture, I. Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 823-826. doi : 10.1016/j.crma.2012.08.002. http://www.numdam.org/articles/10.1016/j.crma.2012.08.002/

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