Weak quantization of Poisson structures
Quantum Algebra
2012-01-24 v3
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.
Cite
@article{arxiv.0707.1978,
title = {Weak quantization of Poisson structures},
author = {Damien Calaque and Gilles Halbout},
journal= {arXiv preprint arXiv:0707.1978},
year = {2012}
}
Comments
LaTex, 19 pages, 6 figures ; typos corrected and references updated