Metric Lie algebras with maximal isotropic centre

2002/09/26 by Ines Kath, Kath, Ines, Martin Olbrich +1 · 2 citations
Mathematics · #17B05 #53C35 #53C50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.DG #math.RA #math.RT #msc:17B05 #msc:53C35 #msc:53C50

paper · pdf · doi:10.48550/arxiv.math/0209366

30 pages; minor corrections

openalex publication_date 2002/09/26 · arxiv created 2002/10/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We 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.

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• Toric geometry of Schouten squares on rotational double extensions
• Metric Lie algebras and quadratic extensions

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