Differential Geometry
Multiplicative Dirac structures on Lie groups
Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1279-1282.

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.

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DOI: 10.1016/j.crma.2008.10.003
Ortiz, Cristián 1

1 Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Rio de Janeiro 22460-320, Brazil
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Ortiz, Cristián. 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. http://www.numdam.org/articles/10.1016/j.crma.2008.10.003/

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