A class of solvable Lie algebras and their Casimir invariants

2004/11/04 by L. Snobl, L Šnobl, P. Winternitz +1 · 6 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #math-ph #math.MP #msc:17B30 #msc:81R05 #nlin.SI

paper · pdf · doi:10.1088/0305-4470/38/12/011

published as J. Phys. A: Math. Gen. 38 (2005) 2687-2700 · 16 pages

arxiv created 2004/11/04 · openalex publication_date 2005/03/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

A nilpotent Lie algebra with an ( n − 1)-dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with as their nilradical are obtained. Their dimension is at most n + 2. The generalized Casimir invariants of and of its solvable extensions are calculated. For n = 4 these algebras figure in the Petrov classification of Einstein spaces. For larger values of n they can be used in a more general classification of Riemannian manifolds.

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• Computation of invariants of Lie algebras by means of moving frames
• Invariants of triangular Lie algebras
• Invariants of solvable lie algebras with triangular nilradicals and diagonal nilindependent elements
• Solvable Lie algebras with Borel nilradicals

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