Proves the solvability of pseudo-Riemannian Lie algebras, suggesting a classification framework.
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 .
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Chen et al. (2012) studied this question.
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