On [formula omitted]-derivations of Lie algebras and corresponding invariant functions

Abstract

We consider finite dimensional complex Lie algebras. We generalize the concept of Lie derivations via certain complex parameters and obtain various Lie and Jordan operator algebras as well as two one-parametric sets of linear operators. Using these parametric sets, we introduce complex functions with a fundamental property — invariance under Lie isomorphisms. One of these basis-independent functions represents a complete set of invariant(s) for three-dimensional Lie algebras. We present also its application to physically motivated examples in dimension 8.