On the compatibility between cup products, the Alekseev–Torossian connection and the Kashiwara–Vergne conjecture, I

Carlo A. Rossi

doi:10.1016/j.crma.2012.08.002

Lie Algebras/Mathematical Physics

On the compatibility between cup products, the Alekseev–Torossian connection and the Kashiwara–Vergne conjecture, I

Presented by: Michèle Vergne

Carlo A. Rossi ¹

¹ MPIM Bonn, Vivatsgasse 7, 53111 Bonn, Germany

Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 823-826.

Abstract
Résumé

For a finite-dimensional Lie algebra $g$ over a field $K \supset C$ , 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 $K \supset C$ . 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.

Received: 2012-06-05
Accepted: 2012-08-07
Published online: 2012-09-01

DOI: 10.1016/j.crma.2012.08.002

Author's affiliations:

Carlo A. Rossi ¹

¹ MPIM Bonn, Vivatsgasse 7, 53111 Bonn, Germany

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     author = {Carlo A. Rossi},
     title = {On the compatibility between cup products, the {Alekseev{\textendash}Torossian} connection and the {Kashiwara{\textendash}Vergne} conjecture, {I}},
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Carlo A. Rossi. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.08.002/

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