Abstract
We give a criterion for a set of Casimir operators of any semisimple Lie algebra to be an algebraically independent generating set of the algebra of the Casimir operators. The criterion is applied to supply complete sets for the Casimir operators of Al, Bl, Cl , and Dl . With the aid of a method to construct some Casimir operators we then furnish complete sets for the Casimir operators of the exceptional Lie algebras using the criterion.