Metric Lie algebras and quadratic extensions

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dc.creatorKath, Ines
dc.creatorOlbrich, Martin
dc.date2003-12-11
dc.date.accessioned2026-07-07T05:03:50Z
dc.date.available2026-07-07T05:03:50Z
dc.descriptionThe present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a non-degenerate invariant symmetric bilinear form. We show that any metric Lie algebra without simple ideals has the structure of a so called balanced quadratic extension of an auxiliary Lie algebra l by an orthogonal l-module A in a canonical way. Identifying equivalence classes of quadratic extensions of l by A with a certain cohomology set H^2_Q(l,A) we obtain a classification scheme for general metric Lie algebras and a complete classification of metric Lie algebras of index 3.
dc.description53 pages
dc.identifierhttps://arxiv.org/abs/math/0312243
dc.identifierhttp://arxiv.org/abs/math/0312243
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69572
dc.subjectDifferential Geometry
dc.subjectRings and Algebras
dc.subjectRepresentation Theory
dc.subject17B05; 53C35; 53C50
dc.titleMetric Lie algebras and quadratic extensions
dc.typetext

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