We extend the representations of finite-dimensional Lie algebra by
derivations of the completed symmetric algebra of its dual to the derivations
of a bigger algebra which includes the exterior algebra on the Lie algebra.
This enables a construction of a twisted version of the exterior differential
calculus with the enveloping algebra in the role of the coordinate algebra. In
this twisted version, the commutators between noncommutative differentials and
coordinates are formal power series in partial derivatives. The square of the
corresponding exterior derivative is zero like in the classical case, but the
Leibniz rule is deformed.