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 
@article{JLT_2012_22_3_JLT_2012_22_3_a6,
     author = {Z. Chen and F. Zhu },
     title = {On {Local} {Structure} of {Pseudo-Riemannian} {Poisson} {Manifolds} and {Pseudo-Riemannian} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {757--767},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JLT_2012_22_3_JLT_2012_22_3_a6/}
}
TY  - JOUR
AU  - Z. Chen
AU  - F. Zhu 
TI  - On Local Structure of Pseudo-Riemannian Poisson Manifolds and Pseudo-Riemannian Lie Algebras
JO  - Journal of Lie theory
PY  - 2012
SP  - 757
EP  - 767
VL  - 22
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JLT_2012_22_3_JLT_2012_22_3_a6/
ID  - JLT_2012_22_3_JLT_2012_22_3_a6
ER  - 
%0 Journal Article
%A Z. Chen
%A F. Zhu 
%T On Local Structure of Pseudo-Riemannian Poisson Manifolds and Pseudo-Riemannian Lie Algebras
%J Journal of Lie theory
%D 2012
%P 757-767
%V 22
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JLT_2012_22_3_JLT_2012_22_3_a6/
%F JLT_2012_22_3_JLT_2012_22_3_a6
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/