Deformation quantization and the action of Poisson vector fields

@article{Sharygin2016DeformationQA,
  title={Deformation quantization and the action of Poisson vector fields},
  author={G. Sharygin},
  journal={Lobachevskii Journal of Mathematics},
  year={2016},
  volume={38},
  pages={1093-1107}
}
  • G. Sharygin
  • Published 2016
  • Mathematics
  • Lobachevskii Journal of Mathematics
As one knows, for every Poisson manifold M there exists a formal noncommutative deformation of the algebra of functions on it; it is determined in a unique way (up to an equivalence relation) by the given Poisson bivector. Let a Lie algebra g act by derivations on the functions on M. The main question, which we shall address in this paper is whether it is possible to lift this action to the derivations on the deformed algebra. It is easy to see, that when dimension of g is 1, the only necessary… Expand
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