A class of solvable Lie algebras and their Casimir Invariants
L. Snobl, P. Winternitz
Abstract
A nilpotent Lie algebra nn,1 with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with nn,1 as their nilradical are obtained. Their dimension is at most n+2. The generalized Casimir invariants of nn,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.
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