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.
Keywords
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}
}
Comments
16 pages