It is shown that a Lie algebra having a nilpotent radical has a fundamental set of invariants consisting of Casimir operators. A different proof is given in the well known special case of an abelian radical. A result relating the number of invariants to the dimension of the Cartan subalgebra is also established.

Keywords:

nilpotent radical, Casimir operators, algebraic Lie algebras, Cartan subalgebras, number of invariants nilpotent radical, Casimir operators, algebraic Lie algebras, Cartan subalgebras, number of invariants

MSC Classifications:

16W25, 17B45, 16S30 show english descriptions Derivations, actions of Lie algebras
Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]
Universal enveloping algebras of Lie algebras [See mainly 17B35] 16W25 - Derivations, actions of Lie algebras
17B45 - Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]
16S30 - Universal enveloping algebras of Lie algebras [See mainly 17B35]

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