On pseudo-Riemannian Lie algebras

Chen, Zhiqi; Ren, Mingming; Zhu, Fuhai

doi:10.1090/S0002-9939-10-10325-6

On pseudo-Riemannian Lie algebras
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by Zhiqi Chen, Mingming Ren and Fuhai Zhu PDF

Proc. Amer. Math. Soc. 138 (2010), 2677-2685 Request permission

Abstract:

In this paper, we show that ${\mathfrak g} {\mathfrak g}\subset {\mathfrak g}$ if ${\mathfrak g}$ is a pseudo-Riemannian Lie algebra with $C(\mathfrak g)\not =0$. Then we show that ${\mathfrak g}{\mathfrak g}\subset {\mathfrak g}$ when $\dim \mathfrak g=4$, which leads to the classification of the pseudo-Riemannian Lie algebras in dimension 4.

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