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.
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Atallah Affane 1
@article{CRMATH_2009__347_21-22_1299_0, author = {Atallah Affane}, title = {Caract\'erisation et existence de structures de {Dirac} multiplicatives}, journal = {Comptes Rendus. Math\'ematique}, pages = {1299--1304}, publisher = {Elsevier}, volume = {347}, number = {21-22}, year = {2009}, doi = {10.1016/j.crma.2009.10.002}, language = {fr}, }
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.002/
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