Publication: Solvable Lie algebras with naturally graded nilradicals and their invariants
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2006
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Iop science
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The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analysed, and their generalized Casimir invariants are 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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