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arXiv · 0707.1978

Weak quantization of Poisson structures

Damien Calaque·Gilles Halbout
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Abstract

In this paper we prove that any Poisson structure on a sheaf of Lie algebroids admits a weak deformation quantization, and give a sufficient condition for such a Poisson structure to admit an actual deformation quantization. We also answer the corresponding classification problems. In the complex symplectic case, we recover in particular some results of Nest-Tsygan and Polesello-Schapira. We begin the paper with a recollection of known facts about deformation theory of cosimplicial differential graded Lie algebras.

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Damien Calaque, Gilles Halbout. 2007-07-13. Weak quantization of Poisson structures. https://doi.org/10.1016/j.geomphys.2011.03.004

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