Multiplicative Dirac structures on Lie groups

Cristián Ortiz

doi:10.1016/j.crma.2008.10.003

Differential Geometry

Multiplicative Dirac structures on Lie groups

Presented by: Charles-Michel Marle

Cristián Ortiz ¹

¹ Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Rio de Janeiro 22460-320, Brazil

Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1279-1282.

Abstract
Résumé

We study multiplicative Dirac structures on Lie groups. We show that the characteristic foliation of a multiplicative Dirac structure is given by the cosets of a normal Lie subgroup and, whenever this subgroup is closed, the leaf space inherits the structure of a Poisson–Lie group. We also describe multiplicative Dirac structures on Lie groups infinitesimally.

Nous étudions les structures de Dirac multiplicatives sur les groupes de Lie. On montre que le feuilletage caractéristique d'une structure de Dirac multiplicative est donnée par les classes à gauche (respectivement à droite) d'un sous-groupe distingué et, quand ce sous-groupe est fermé, l'espace des feuilles est muni d'une structure de groupe de Lie–Poisson. Nous décrivons aussi la version infinitésimale des structures de Dirac multiplicatives sur les groupes de Lie.

Received: 2008-02-18
Accepted: 2008-10-08
Published online: 2008-11-01

DOI: 10.1016/j.crma.2008.10.003

Author's affiliations:

Cristián Ortiz ¹

¹ Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Rio de Janeiro 22460-320, Brazil

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     author = {Cristi\'an Ortiz},
     title = {Multiplicative {Dirac} structures on {Lie} groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1279--1282},
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     volume = {346},
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     year = {2008},
     doi = {10.1016/j.crma.2008.10.003},
     language = {en},
}

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Cristián Ortiz. Multiplicative Dirac structures on Lie groups. Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1279-1282. doi : 10.1016/j.crma.2008.10.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.10.003/

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