Casimir operators and nilpotent radicals
type: Item
instance of: scholarly article
zbMATH Open document ID: 1257.17026
DOI: 10.4153/CMB-2011-102-2
published in: Canadian Mathematical Bulletin
publication date: 2012-09-06T00:00:00Z
Mathematics Subject Classification ID: 17B45
zbMATH DE Number: 6078235
zbMATH Keywords: nilpotent radical
zbMATH Keywords: Casimir operators
zbMATH Keywords: algebraic Lie algebras
zbMATH Keywords: Cartan subalgebras
zbMATH Keywords: number of invariants
author: J. C. Ndogmo
MaRDI profile type: Publication
title: Casimir operators and nilpotent radicals
review text: Using the properties of algebraic Lie algebras and some results on enveloping algebras [\textit{J. Dixmier}, Algèbres enveloppantes. Paris etc.: Gauthier-Villars (1974; Zbl 0308.17007)], in this paper it is shown that Lie algebras possessing a nilpotent radical have a fundamental set of invariants that can be chosen as polynomials. The author also comments on the possibility of extending the result to those solvable non-nilpotent Lie algebras admitting polynomial invariants, whose characterization is yet unknown. In addition, it is analyzed under which conditions the number of invariants coincides with the rank of the Levi subalgebra when the latter is isomorphic to \(\mathfrak{sl}(2)\).
reviewed by: Rutwig Campoamor Stursberg
description: scientific article; zbMATH DE number 6078235