A remark on nonequivalent star products via reduction for CPn

In this Letter, we construct nonequivalent star products on CPn by phase space reduction. It turns out that the nonequivalent star products occur very natural in the context of phase space reduction by deforming the momentum map of the U(1)-action on Cn+1\[O] into a quantum momentum map and the corresponding momentum value into a quantum momentum value such that the level set, i.e. the 'constraint surface', of the quantum momentum map coincides with the classical one. All equivalence classes of star products on CPn are obtained by this construction.