Solvable Lie algebras with naturally graded nilradicals and their invariants

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.

References in corpus (3)

• A class of solvable Lie algebras and their Casimir Invariants
• Invariants of the nilpotent and solvable triangular Lie algebras
• On the invariants of some solvable rigid Lie algebras

Cited by in corpus (11)

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• Invariants of Lie Algebras with Fixed Structure of Nilradicals
• Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements
• On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras
• Invariants of Triangular Lie Algebras
• Solvable Lie algebras with Borel nilradicals
• Invariants of triangular Lie algebras with one nilindependent diagonal element
• Contact Lie systems on Riemannian and Lorentzian spaces: from scaling symmetries to curvature-dependent reductions