**Twisted Cocycles of Lie Algebras and Corresponding Invariant Functions**

**Abstract:**

We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept
of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint
representation - derivations. In
this case we obtain various Lie and Jordan operator algebras and two one-parametric sets of linear operators. These and
similar parametric sets for higher-dimensional cocycles allow us to define complex functions which are invariant under Lie
isomorphisms. Such complex functions thus represent useful invariants - we show how they classify three and
four-dimensional Lie algebras as well as how they apply to some eight-dimensional one-parametric nilpotent continua of Lie
algebras. These functions also provide necessary
criteria for existence of 1-parametric continuous contraction.