Algebraic Symplectic Reduction and Quantization of Singular Spaces

The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of singular Poisson spaces Grdnewold-Moyal series is explic-itly constructed and convergence is checked. Some examples of deformation quantization of singular Poisson spaces are considered in detail.