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arXiv · 1204.4787

Solvable quadratic Lie algebras in low dimensions

Tien Dat Pham·Anh Vu Le·Minh Thanh Duong
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Abstract

In this paper, we classify solvable quadratic Lie algebras up to dimension 6. In dimensions smaller than 6, we use the Witt decomposition given in \cite{Bou59} and a result in \cite{PU07} to obtain two non-Abelian indecomposable solvable quadratic Lie algebras. In the case of dimension 6, by applying the method of double extension given in \cite{Kac85} and \cite{MR85} and the classification result of singular quadratic Lie algebras in \cite{DPU}, we have three families of solvable quadratic Lie algebras which are indecomposable and not isomorphic.

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Tien Dat Pham, Anh Vu Le, Minh Thanh Duong. 2012-04-21. Solvable quadratic Lie algebras in low dimensions. https://arxiv.org/abs/1204.4787

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