Kath, Ines; Olbrich, Martin Metric Lie algebras with maximal isotropic centre. (English) Zbl 1046.17003 Math. Z. 246, No. 1-2, 23-53 (2004). The authors are interested in the classification of metric Lie algebras, that is, of finite-dimensional real Lie algebras equipped with an invariant non-degenerate symmetric bilinear form. In the present paper they determine the isomorphism classes of a certain type of solvable metric Lie algebras. They show that every metric Lie algebra of this type is a two-fold extension associated with an orthogonal representation of an abelian Lie algebra. The equivalence classes of such extensions are described by a certain cohomology set. As an application they obtain a classification scheme for metric Lie algebras with maximal isotropic center and the classification of metric Lie algebras of index 2. Reviewer: Jürgen Berndt (Cork) Cited in 10 Documents MSC: 17B05 Structure theory for Lie algebras and superalgebras 53C35 Differential geometry of symmetric spaces Keywords:solvable Lie algebra; metric Lie algebra; orthogonal representations of abelian Lie algebras; Lie algebras of index 2; Lie algebras with maximal isotropic center PDFBibTeX XMLCite \textit{I. Kath} and \textit{M. Olbrich}, Math. Z. 246, No. 1--2, 23--53 (2004; Zbl 1046.17003) Full Text: DOI arXiv