Abstract
Let P be a Poisson G-space and Λ a classical triangular r-matrix. Using the Poisson reduction, we construct a new Poisson structure P Λ on P. For this new Poisson structure P Λ , we construct its symplectic groupoid, describe its symplectic leaves, and classify its symplectic realizations. The deformation quantization of P Λ is also discussed.
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