Ortiz, Cristián Multiplicative Dirac structures on Lie groups. (English. Abridged French version) Zbl 1163.53052 C. R., Math., Acad. Sci. Paris 346, No. 23-24, 1279-1282 (2008). One introduces the notion of multiplicative Dirac structure on a Lie group \(G\) and investigates some of its basic properties. Specifically, a Dirac structure \(L\) on \(G\) is multiplicative if \(L\) is a subgroupoid of \(TG\oplus T^*G\). In the special case of Poisson structures, one recovers the notion of Poisson Lie group. In the general case, one proves that a regular involutive distribution on \(TG\) induces a multiplicative Dirac structure if and only if it is defined by a normal subgroup of \(G\). One then uses this property in order to study the characteristic foliation and the multiplicative Poisson structure on the corresponding leaf space for a multiplicative Dirac structure on \(G\). Reviewer: Daniel Beltiţă (Bucureşti) Cited in 1 ReviewCited in 9 Documents MSC: 53D17 Poisson manifolds; Poisson groupoids and algebroids 53C30 Differential geometry of homogeneous manifolds Keywords:Dirac structure; characteristic foliation; Poisson Lie group × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link References: [1] Bursztyn, H.; Radko, O., Gauge equivalence of Dirac structures and symplectic groupoids, Ann. Inst. Fourier (Grenoble), 53, 309-337 (2003) · Zbl 1026.58019 [2] Courant, T., Dirac manifolds, Trans. Amer. Math. Soc., 319, 631-661 (1990) · Zbl 0850.70212 [3] Courant, T.; Weinstein, A., Beyond Poisson structures, (Action hamiltonnienes de groupes. Troisieme théorème the Lie. Action hamiltonnienes de groupes. Troisieme théorème the Lie, Lyon, 1986 (1988), Hermann: Hermann Paris), 39-49 · Zbl 0698.58020 [4] Drinfeld, V., Hamiltonian structures on Lie groups, Lie bialgebras and geometric meaning of the classical Yang-Baxter equations, Soviet Math. Dokl., 27, 1, 68-71 (1983) · Zbl 0526.58017 [5] Lu, J. H.; Weinstein, A., Poisson Lie groups, dressing transformations, and Bruhat decompositions, J. Differential Geometry, 31, 501-526 (1990) · Zbl 0673.58018 [6] Mackenzie, K., General Theory of Lie Groupoids and Lie Algebroids, London Math. Soc. Lecture Notes Ser., vol. 213 (2005) · Zbl 1078.58011 [7] Semenov-Tian-Shansky, M., Dressing transformation and Poisson-Lie group actions, Publ. RIMS, Kyoto University, 21, 1237-1260 (1985) · Zbl 0673.58019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.