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Solvable Lie algebras with naturally graded nilradicals and their invariants

J M Ancochea, R Campoamor-Stursberg, L Garcia Vergnolle

math-pharXiv:math-ph/0511027

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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