Caractérisation et existence de structures de Dirac multiplicatives

Atallah Affane

doi:10.1016/j.crma.2009.10.002

Géométrie différentielle

Caractérisation et existence de structures de Dirac multiplicatives
[Characterization and existence of multiplicative Dirac structures]

Presented by: Charles-Michel Marle

Atallah Affane ¹

¹ Faculté de mathématiques, USTHB, B.P. 32 El Alia Bab Ezzouar, Alger, Algérie

Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1299-1304

Résumé (Original language)
Abstract

Nous définissons le produit de deux variétés de Dirac et la notion de groupe de Dirac–Lie de type Poisson. Cette notion est équivalente à celle de structure de Dirac multiplicative et tout groupe de Lie réel simplement connexe, de dimension au moins 2 porte une structure de Dirac multiplicative non triviale.

We define the product of two Dirac manifolds and introduce the notion of a Dirac–Lie group of Poisson type. This notion is equivalent to that of multiplicative Dirac structure and any real simply-connected Lie group carries a no trivial multiplicative Dirac structure when its dimension is at least 2.

Received: 2009-09-14
Accepted: 2009-10-02
Published online: 2009-10-21

DOI: 10.1016/j.crma.2009.10.002

Author's affiliations:

Atallah Affane ¹

¹ Faculté de mathématiques, USTHB, B.P. 32 El Alia Bab Ezzouar, Alger, Algérie

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Atallah Affane. Caractérisation et existence de structures de Dirac multiplicatives. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1299-1304. doi: 10.1016/j.crma.2009.10.002

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