Weak quantization of Poisson structures

Details Weak quantization of Poisson structures Weak quantization of Poisson structures

2007-07-13

arxiv.org/abs/0707.1978v3

Journal of Geometry and Physics 61 (2011), no. 8, 1401-1414

Mathematics

Quantum Algebra

LaTex, 19 pages, 6 figures ; typos corrected and references updated

Scientific paper

10.1016/j.geomphys.2011.03.004

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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