Deformation Quantization of Poisson Manifolds

@article{Kontsevich1997DeformationQO,
  title={Deformation Quantization of Poisson Manifolds},
  author={Maxim Kontsevich},
  journal={Letters in Mathematical Physics},
  year={1997},
  volume={66},
  pages={157-216}
}
  • M. Kontsevich
  • Published 29 September 1997
  • Mathematics
  • Letters in Mathematical Physics
I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one correspondence with the set of equivalence classes of Poisson structures on X modulo diffeomorphisms. In fact, a more general statement is proven (the ‘Formality conjecture’), relating the Lie superalgebra of polyvector fields on X and the Hochschild complex… 
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