SOLVABLE QUADRATIC LIE ALGEBRAS IN LOW DIMENSIONS

Abstract

In this paper, we classify solvable quadratic Lie algebras up to di

mension 6. In cases of dimensions smaller than 6, we use the Witt de

composition given in [4] and a result in [12] to obtain two non-Abelian

indecomposable solvable quadratic Lie algebras. In the case of dimen

sion 6, by applying the method of double extension given in [7] and [11]

and the classification result of singular quadratic Lie algebras in [6], we

obtain three families of indecomposable solvable quadratic Lie algebras.