Deformation Quantization of Polynomial Poisson Algebras

@inproceedings{Penkava1998DeformationQO,
  title={Deformation Quantization of Polynomial Poisson Algebras},
  author={Michael Penkava and Pol Vanhaecke},
  year={1998}
}
This paper discusses the notion of a deformation quantization for an arbitrary polynomial Poisson algebra A. We examine the Hochschild coho-mology group H 3 (A) and find that if a deformation of A exists it can be given by bidifferential operators. We then compute an explicit third order deformation quantization of A and show that it comes from a quantized enveloping algebra. We show that the deformation extends to a fourth order deformation if and only if the quantized enveloping algebra gives… CONTINUE READING

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