  Using the fact that the algebra M(3,C) of 3 x 3 complex matrices can be taken
as a reduced quantum plane, we build a differential calculus Omega(S) on the
quantum space S defined by the algebra C^\infty(M) \otimes M(3,C), where M is a
space-time manifold. This calculus is covariant under the action and coaction
of finite dimensional dual quantum groups. We study the star structures on
these quantum groups and the compatible one in M(3,C). This leads to an
invariant scalar product on the later space. We analyse the differential
algebra Omega(M(3,C)) in terms of quantum group representations, and consider
in particular the space of one-forms on S since its elements can be considered
as generalized gauge fields.
