A class of solvable Lie algebras and their Casimir Invariants

Details A class of solvable Lie algebras and their Casimir Invariants A class of solvable Lie algebras and their Casimir Invariants

2004-11-04

arxiv.org/abs/math-ph/0411023v1

J. Phys. A: Math. Gen. 38 (2005) 2687-2700

Physics

Mathematical Physics

16 pages

Scientific paper

10.1088/0305-4470/38/12/011

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

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