Geodesic
On Local Structure of Pseudo-Riemannian Poisson Manifolds and Pseudo-Riemannian Lie Algebras
Journal of Lie theory, Tome 22 (2012) no. 3, pp. 757-767.

Voir la notice de l'article provenant de la source Heldermann Verlag

Pseudo-Riemannian Poisson manifolds and pseudo-Riemannian Lie algebras were introduced by M. Boucetta. In this paper, we prove that all pseudo-Riemannian Lie algebras are solvable. Based on our main result and some properties of pseudo-Riemannian Lie algebras, we classify Riemann-Lie algebras of arbitrary dimension and pseudo-Riemannian Lie algebras of dimension at most 3.
Classification : 53D17, 22E50, 17D25
Mots-clés : Levi decomposition, pseudo-Riemannian Poisson manifold, pseudo-Riemannian Lie algebra 
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Z. Chen; F. Zhu . On Local Structure of Pseudo-Riemannian Poisson Manifolds and Pseudo-Riemannian Lie Algebras. Journal of Lie theory, Tome 22 (2012) no. 3, pp. 757-767. http://geodesic.mathdoc.fr/item/JLT_2012_22_3_JLT_2012_22_3_a6/