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As a specialist told me, given a smooth affine Poisson algebra $S$ over $\mathbb{C}$, up to a choice of certain characteristic class, one can find one of the deformation quantizations of $S$, say $A$, ...

I work entirely over a field of characteristic $0$, in case it matters. Recall that a Poisson algebra is a commutative algebra $A$ with a bracket $\lbrace,\rbrace : A^{\wedge 2} \to A$ which is (1) a ...

Background: in deformation quantization one wants to construct formal associative deformations (the star products $\star$) of the algebra of smooth complex-valued functions on a Poisson manifold $M$ ...