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Solvable Lie algebras with naturally graded nilradicals and their invariants

J M Ancochea·R Campoamor-Stursberg·L Garcia Vergnolle
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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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J M Ancochea, R Campoamor-Stursberg, L Garcia Vergnolle. 2006-02-01. Solvable Lie algebras with naturally graded nilradicals and their invariants. https://doi.org/10.1088/0305-4470/39/6/008

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