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.
1
School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China
Zhiqi Chen; Fuhai 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/JOLT_2012_22_3_a6/
@article{JOLT_2012_22_3_a6,
author = {Zhiqi Chen and Fuhai Zhu},
title = {On {Local} {Structure} of {Pseudo-Riemannian} {Poisson} {Manifolds} and {Pseudo-Riemannian} {Lie} {Algebras}},
journal = {Journal of Lie Theory},
pages = {757--767},
year = {2012},
volume = {22},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2012_22_3_a6/}
}
TY - JOUR
AU - Zhiqi Chen
AU - Fuhai 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
UR - http://geodesic.mathdoc.fr/item/JOLT_2012_22_3_a6/
ID - JOLT_2012_22_3_a6
ER -
%0 Journal Article
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%A Fuhai 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
%U http://geodesic.mathdoc.fr/item/JOLT_2012_22_3_a6/
%F JOLT_2012_22_3_a6
