SOLVABLE QUADRATIC LIE ALGEBRAS IN LOW DIMENSIONS

Abstract

In this paper, we classify solvable quadratic Lie algebras up to dimension 6. In cases of dimensions smaller than 6, we use the Witt decomposition given in [4] and a result in [12] 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 [7] and [11] and the classification result of singular quadratic Lie algebras in [6], we obtain three families of indecomposable solvable quadratic Lie algebras.