  The problem of finding generators of the subalgebra of invariants under the
action of a group of automorphisms of a finite dimensional Lie algebra on its
universal enveloping algebra is reduced to finding homogeneous generators of
the same group acting on the symmetric tensor algebra of the Lie algebra. This
process is applied to prove a constructive Hilbert-Nagata Theorem (including
degree bounds) for the algebra of invariants in a Lie nilpotent relatively free
associative algebra endowed with an action induced by a representation of a
reductive group.
