Casimir operators of Lie algebras with a nilpotent radical

TL;DR

This paper proves that Lie algebras with a nilpotent radical possess a fundamental set of Casimir invariants, providing a new proof for the case where the radical is abelian.

Contribution

It establishes the existence of Casimir invariants for Lie algebras with nilpotent radicals and offers a novel proof for the abelian radical case.

Findings

Lie algebras with nilpotent radical have fundamental Casimir invariants

Provided a new proof for the abelian radical case

Confirmed the structure of invariants in these Lie algebras

Abstract

We show that a Lie algebra having a nilpotent radical has a fundamental set of invariants consisting of Casimir operators. We give a different proof of this fact in the special and well-known case where the radical is abelian.