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Solvable Lie algebras with naturally graded nilradicals and their invariants

Ancochea Bermúdez , José María and Campoamor Stursberg, Otto Ruttwig and Vergnolle, L.G. (2006) Solvable Lie algebras with naturally graded nilradicals and their invariants. Journal of physics A: Mathematical and general, 39 (6). pp. 1339-1355. ISSN 0305-4470

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Casimir-operators; Nilpotent
Subjects:Sciences > Mathematics > Group Theory
ID Code:14718
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