Weak quantization of Poisson structures

作者：Calaque Damien^*; Halbout Gilles

来源：Journal of Geometry and Physics, 2011, 61(8): 1401-1414.

DOI：10.1016/j.geomphys.2011.03.004

• Deformation quantization
• Formality theorems
• Holomorphic Poisson structures
• Algebroid stacks
• Lie algebroids

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.

• 出版日期2011-8