Strict quantization of polynomial Poisson structures (Q2692763)

In this paper, the authors show how combinatorial star products can be used to obtain deformation quantizations of polynomial Poisson structures. First, the authors review the relevant background for star products and introduce the notion of combinatorial star products. Then the main result is proved, which generalizes results for constant and linear Poisson structures to polynomial Poisson structures of arbitrary degree. Several examples of nonlinear Poisson structures are given and their formal star products are explicitly constructed. Finally, the authors discuss further questions such as realizations of the strict quantization.