  We construct a universal envelope for any Poisson- and Gerstenhaber algebra.
While the deformation theory of Poisson algebras seems to be partially trivial,
results from string- and M-theory suggest a rich deformation theory of
Gerstenhaber algebras. We apply our construction in this case to well known
questions on the topological closed string BRST-complex. Finally, we find a
similar algebraic structure, as for the universal envelope, in the SU(2)-WZW
model.
