2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65090We investigate a certain class of solvable metric Lie algebras. For this purpose a theory of twofold extensions associated to an orthogonal representation of an abelian Lie algebra is developed. Among other things, we obtain a classification scheme for indecomposable metric Lie algebras with maximal isotropic centre and the classification of metric Lie algebras of index 2.30 pages; minor correctionsDifferential GeometryRings and AlgebrasRepresentation Theory17B05;53C35;53C50text