## A remark on nonequivalent star products via reduction for $$\mathbb{C}\mathbb{P}^n$$.(English)Zbl 0924.58119

Summary: We construct nonequivalent star products on $$\mathbb{C}\mathbb{P}^n$$ 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 $$\mathbb{C}^{n-1}\setminus\{0\}$$ 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 $$\mathbb{C}\mathbb{P}^n$$ are obtained by this construction.

### MSC:

 58H15 Deformations of general structures on manifolds 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
Full Text: