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arXiv · 1310.6415

Quantization of Whitney functions and reduction

Markus J. Pflaum·Hessel Posthuma·Xiang Tang
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Abstract

For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is a subset of a not necessarily regular Poisson manifold which can be written as the quotient of a regular Poisson manifold on which a compact Lie group acts freely by Poisson maps. Finally, if the quotient Poisson manifold is regular as well, we show a "quantization commutes with reduction" type result. For the proofs, we use methods stemming from both singularity theory and Poisson geometry.

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Markus J. Pflaum, Hessel Posthuma, Xiang Tang. 2013-10-23. Quantization of Whitney functions and reduction. https://arxiv.org/abs/1310.6415

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