On the quantization of Poisson brackets

  title={On the quantization of Poisson brackets},
  author={Joseph Donin},
In this paper we introduce two classes of Poisson brackets on algebras (or on sheaves of algebras). We call them locally free and nonsingular Poisson brackets. Using the Fedosov’s method we prove that any locally free nonsingular Poisson bracket can be quantized. In particular, it follows from this that all Poisson brackets on an arbitrary field of characteristic zero can be quantized. The well known theorem about the quantization of nondegenerate Poisson brackets on smooth manifolds follows… CONTINUE READING

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Majid , Rmatrix brackets and their quantization

  • D. Gurevich J. Donin, S.
  • Preprint , Bar - Ilan Univ .
  • 1992

Makar - Limanov , On quadratic Poisson brackets on a polynomial ring F [ x , y , z ]

  • J. Donin, L.
  • NATO - ASI Series Proc . of Int . Congress of…
  • 1986

Sternheimer , Deformation theory and quantization

  • F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D.
  • Ann . Physics
  • 1978

Lecomte , Formal deformations of the Poisson Lie algebra of a symplectic manifold and starproducts , “ Deformation Theory of Algebra and Structures and Applications ”

  • M. de Wilde, P.
  • Complexe Cotangent et Déformations I ” , Lecture…
  • 1971

Algebraic Cohomology and Deformation Theory , “ Deformation Theory of Algebra and Structures and Applications ”

  • M. Gerstenhaber, S. D. Schack
  • On the deformation of Rings and Algebras III…

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