Strict Quantization of Polynomial Poisson Structures

We show how combinatorial star products can be used to obtain strict deformation quantizations of polynomial Poisson structures on $\mathbb R^d$, generalizing known results for constant and linear arbitrary degree. give several examples nonlinear construct explicit formal whose parameter evaluated any real value $\hbar$, giving the space analytic functions R^d$ with infinite radius convergence. also address further questions such as continuity classical limit $\hbar \to 0$, compatibility *-involutions, existence positive functionals. The latter realize *-algebras operators a pre-Hilbert which we demonstrate in concrete example.