Deformation Quantization of Polynomial Poisson Algebras

  title={Deformation Quantization of Polynomial Poisson Algebras},
  author={Michael Penkava and Pol Vanhaecke},
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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Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 19 references

Deformation quantization of Poisson manifolds, I, Preprint:q-alg/9709040

  • M Kontsevich
  • Deformation quantization of Poisson manifolds, I…
  • 1997

Integrable systems in the realm of algebraic geometry

  • P Vanhaecke
  • Lecture Notes in Mathematics
  • 1996

A Poincaré-Birkhoff-Witt theorem for infinite dimensional Lie algebras

  • Journal of the Mathematical Society of Japan
  • 1994

A guide to quantum groups

  • V Chari, A Pressley
  • A guide to quantum groups
  • 1994

A simple geometric construction of deformation quantization

  • B V Fedosov
  • J. Diff. Geom
  • 1994

A construction of a deformation quantization of a Poisson algebra, Geometry and Its Applications (Singapore) Deformation quantizations of Poisson algebras

  • H Omori, Y Maeda, A Yoshioka
  • World Scientific Contemporary Mathematics
  • 1993


  • J Huebschmann, J Reine Poisson Cohomology And Quantization, Angew
  • Math
  • 1990

On some unsolved problems in quantum group theory, Quantum groups, Proceedings of Workshops held in the Euler International Mathematical Institute

  • V G Drinfeld
  • Lecture Notes in Mathematics
  • 1990

Non-linear Poisson structures and R-matrices

  • S Li, L Parmentier
  • Comm. Math. Phys
  • 1989

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