Solvable Lie algebras with naturally graded nilradicals and their invariants

Details Solvable Lie algebras with naturally graded nilradicals and their invariants Solvable Lie algebras with naturally graded nilradicals and their invariants

2005-11-07

arxiv.org/abs/math-ph/0511027v2

J. Phys. A: Math. Gen. 39 (2006), 1339-1355

Physics

Mathematical Physics

Scientific paper

10.1088/0305-4470/39/6/008

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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