  In quantum groups coproducts of Lie-algebras are twisted in terms of
generators of the corresponding universal enveloping algebra. If
representations are considered, twists also serve as starproducts that
accordingly quantize representation spaces. In physics, requirements turn out
to be the other way around. Physics comes up with noncommutative spaces in
terms of starproducts that miss a suiting quantum symmetry. In general the
classical limit is known, i.e. there exists a representation of the Lie-algebra
on a corresponding finitely generated commutative space. In this setup
quantization can be considered independently from any representation theoretic
issue. We construct an algebra of vector fields from a left cross-product
algebra of the representation space and its Hopf-algebra of momenta. The latter
can always be defined. The suitingly devided cross-product algebra is then
lifted to a Hopf-algebra that carries the required genuine structure to
accomodate a matrix representation of the universal enveloping algebra as a
subalgebra. We twist the Hopf-algebra of vector fields and thereby obtain the
desired twisting of the Lie-algebra. Since we twist with vector fields and not
with generators of the Lie-algebra, this is the most general twisting that can
possibly be obtained. In other words, we push starproducts to twists of the
desired symmetry algebra and to this purpose solve the problem of turning
vector fields into a Hopf-algebra. We give some genuine example.
