  Perturbative deformations of symmetry structures on noncommutative spaces are
studied in view of noncommutative quantum field theories. The rigidity of
enveloping algebras of semi-simple Lie algebras with respect to formal
deformations is reviewed in the context of star products. It is shown that
rigidity of symmetry algebras extends to rigidity of the action of the symmetry
on the space. This implies that the noncommutative spaces considered can be
realized as star products by particular ordering prescriptions which are
compatible with the symmetry. These symmetry preserving ordering prescriptions
are calculated for the quantum plane and four-dimensional quantum Euclidean
space. Using these ordering prescriptions greatly facilitates the construction
of invariant Lagrangians for quantum field theory on noncommutative spaces with
a deformed symmetry.
