1. CMB 2011 (vol 55 pp. 579)
|Casimir Operators and Nilpotent Radicals|
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
Categories:16W25, 17B45, 16S30