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Letters in Mathematical Physics

, Volume 77, Issue 2, pp 199–208 | Cite as

Poisson Actions up to Homotopy and their Quantization

  • Pavol Ševera
Article

Abstract

Symmetries of Poisson manifolds are in general quantized just to symmetries up to homotopy of the quantized algebra of functions. It is therefore interesting to study symmetries up to homotopy of Poisson manifolds. We notice that they are equivalent to Poisson principal bundles and describe their quantization to symmetries up to homotopy of the quantized algebras of functions, using the formality theorem of Kontsevich.

Keywords

Poisson manifolds actions up to homotopy moment maps deformation quantization 

Mathematics Subject Classification (2000)

53D17 53D55 53D20 

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Section de MathètiquesUniversité de GenèveGenèveSwitzerland
  2. 2.Department of Theoretical PhysicsBratislavaSlovakia

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