UNIVERSAL DEFORMATION FORMULAS AND BREAKING SYMMETRY

We show that an algebra with a non-nilpotent Lie group of automorphism s or ''symmetries'' (e.g., smooth functions on a manifold with such a group of diffeomorphisms) may generally be deformed (in the function c ase, ''quantized'') in such a way that only a proper subgroup of the o riginal group acts. This symmetry breaking is a consequence of the exi stence of certain ''universal deformation formulas'' which are element s, independent of the original algebra, in the tensor algebra of the e nveloping algebra of the Lie algebra of the group.