Geodesic
On Riemann-Poisson Lie groups
Archivum mathematicum, Tome 56 (2020) no. 4, pp. 225-247.

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A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in [4]. We study these Lie groups and we give a characterization of their Lie algebras. We give also a way of building these Lie algebras and we give the list of such Lie algebras up to dimension 5.
DOI : 10.5817/AM2020-4-225
Classification : 22E05, 53A15, 53D17
Keywords: Lie group; Poisson manifolds; Riemannian metric 
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Alioune, Brahim; Boucetta, Mohamed; Sid’Ahmed Lessiad, Ahmed. On Riemann-Poisson Lie groups. Archivum mathematicum, Tome 56 (2020) no. 4, pp. 225-247. doi : 10.5817/AM2020-4-225. http://geodesic.mathdoc.fr/articles/10.5817/AM2020-4-225/

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