Metric Lie algebras with maximal isotropic centre
type: Item
instance of: scholarly article
title: Metric Lie algebras with maximal isotropic centre
zbMATH Open document ID: 1046.17003
author: Ines Kath
author: Martin Olbrich
published in: Mathematische Zeitschrift
publication date: 2004-07-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0209366
review text: The authors are interested in the classification of metric Lie algebras, that is, of finite-dimension\-al 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.
reviewed by: Jürgen Berndt
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 2078040
zbMATH Keywords: solvable Lie algebra
zbMATH Keywords: metric Lie algebra
zbMATH Keywords: orthogonal representations of abelian Lie algebras
zbMATH Keywords: Lie algebras of index 2
zbMATH Keywords: Lie algebras with maximal isotropic center
MaRDI profile type: Publication
OpenAlex ID: W2125270514
arXiv ID: math/0209366
DOI: 10.1007/S00209-003-0575-2
description: scientific article