  We analyze the star product induced on the algebra of functions on R^3 by a
suitable reduction of the Moyal product defined on F(R^4). This is obtained
through the identification of R^3 with the dual of a three dimensional Lie
algebra.
  We consider the su(2) case, exhibit a matrix basis and realize the algebra of
functions on its dual in such a basis. The relation to the Duflo map is
discussed. As an application to quantum mechanics we compute the spectrum of
the hydrogen atom.
