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Deformation quantization of infinite dimensional Poisson manifolds
In 1999, Karaali wrote a review of formal deformation quantization for a class she took with Weinstein.
She ends the paper with the following remark:
Another question that remains involves the ...
7
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answers
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Could we extend the star product on a Poisson manifold from its ring of smooth functions to its de Rham complex?
Let $M$ be a smooth manifold with a Poisson bracket $\{-,-\}$. Kontsevich proved that there exists a deformation quantization of $M$, i.e. let $C^{\infty}(M)[[\hbar]]=C^{\infty}(M)\otimes_{\mathbb{R}}\...