Ancochea Bermúdez, José MaríaCampoamor Stursberg, Otto-RudwigVergnolle, L. G.2023-06-202023-06-2020060305-447010.1088/0305-4470/39/6/008https://hdl.handle.net/20.500.14352/49809The 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.engjournal articlehttps//doi.org/10.1088/0305-4470/39/6/008http://iopscience.iop.org/0305-4470/39/6/008/restricted access512.544.33Casimir-operatorsNilpotentGrupos (Matemáticas)