Solvable quadratic Lie algebras in low dimensions
Rings and Algebras
2012-04-24 v1
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.
Cite
@article{arxiv.1204.4787,
title = {Solvable quadratic Lie algebras in low dimensions},
author = {Tien Dat Pham and Anh Vu Le and Minh Thanh Duong},
journal= {arXiv preprint arXiv:1204.4787},
year = {2012}
}
Comments
10 pages