English

A class of solvable Lie algebras and their Casimir Invariants

Mathematical Physics 2007-05-23 v1 math.MP Exactly Solvable and Integrable Systems

Abstract

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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Cite

@article{arxiv.math-ph/0411023,
  title  = {A class of solvable Lie algebras and their Casimir Invariants},
  author = {L. Snobl and P. Winternitz},
  journal= {arXiv preprint arXiv:math-ph/0411023},
  year   = {2007}
}

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16 pages