A class of solvable Lie algebras and their Casimir invariants

doi:10.1088/0305-4470/38/12/011

A class of solvable Lie algebras and their Casimir invariants

L Šnobl et al 2005 J. Phys. A: Math. Gen. 38 2687-2700 doi: 10.1088/0305-4470/38/12/011

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L Šnobl^1,2 and P Winternitz³
¹ Centre de recherches mathématiques, Université de Montréal, CP 6128, Succ Centre-Ville, Montréal (Québec) H3C 3J7, Canada
² Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Břehová 7, 115 19 Prague 1, Czech Republic
³ Centre de recherches mathématiques and Departement de mathématiques et de statistique, Université de Montréal, CP 6128, Succ Centre-Ville, Montréal (Québec) H3C 3J7, Canada
E-mail: Libor.Snobl@fjfi.cvut.cz and wintern@crm.umontreal.ca

Abstract. A nilpotent Lie algebra ${\mathfrak n}_{n,1}$ with an (n − 1)-dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with ${\mathfrak n}_{n,1}$ as their nilradical are obtained. Their dimension is at most n + 2. The generalized Casimir invariants of ${\mathfrak n}_{n,1}$ 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.

PACS numbers: 02.20.Qs, 03.65.Fd, 04.50.+h

Print publication: Issue 12 (25 March 2005)
Received 4 November 2004, in final form 4 February 2005
Published 9 March 2005

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A class of solvable Lie algebras and their Casimir invariants

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