A class of solvable Lie algebras and their Casimir invariants

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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