Solvable Lie algebras with naturally graded nilradicals and their invariants
J M AncocheaDepartamento Geometría y Topología, Fac. CC. Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, E-28040 Madrid, SpainR Campoamor-StursbergDepartamento Geometría y Topología, Fac. CC. Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, E-28040 Madrid, SpainL Garcia VergnolleDepartamento Geometría y Topología, Fac. CC. Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, E-28040 Madrid, Spain
2006en
ABI
Abstract
The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable algebras have a contact form, which implies the existence of an associated dynamical system. Moreover, due to the structure of the quadratic Casimir operator of the nilradical, these algebras contain a maximal non-abelian quasi-classical Lie algebra of dimension $2n-1$, indicating that gauge theories (with ghosts) are possible on these subalgebras.
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