L Šnobl and P Winternitz 2005 J. Phys. A: Math. Gen. 38 2687 doi:10.1088/0305-4470/38/12/011
A class of solvable Lie algebras and their Casimir invariants
L Šnobl1,2 and P Winternitz3
Show affiliationsA 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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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
L Šnobl and P Winternitz 2005 J. Phys. A: Math. Gen. 38 2687
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