Journal of Lie Theory

no. 3
On Local Structure of Pseudo-Riemannian Poisson Manifolds and Pseudo-Riemannian Lie Algebras
Zhiqi Chen1; Fuhai Zhu1
1School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China
Journal of Lie Theory, Volume 22 (2012) no. 3, pp. 757-767
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.
DOI: 10.5802/jolt.690
Classification: 53D17, 22E50, 17D25
Keywords: Levi decomposition, pseudo-Riemannian Poisson manifold, pseudo-Riemannian Lie algebra

Zhiqi Chen  1 ; Fuhai Zhu  1

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, Volume 22 (2012) no. 3, pp. 757-767. doi: 10.5802/jolt.690
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     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},
     doi = {10.5802/jolt.690},
     zbl = {1267.53089},
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}
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