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Letters in Mathematical Physics

, Volume 82, Issue 2–3, pp 177–189 | Cite as

Poisson Action and Formality

  • Didier Arnal
  • Najla Dahmene
  • Khaled Tounsi
Article
  • 44 Downloads

Abstract

Using a formality on a Poisson manifold, we construct a star product and for each Poisson vector field a derivation of this star product. Starting with a Poisson action of a Lie group, we are able under a natural cohomological assumption to define a representation of its Lie algebra in the space of derivations of the star product. Finally, we use these results to define some generically tangential star products on duals of Lie algebra as in [1] but in a more realistic context.

Mathematics Subject Classification (2000)

46L65 53D17 58D19 

Keywords

formality deformation quantization Poisson manifold 

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References

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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijon CedexFrance
  2. 2.Faculté des sciences de GabesGabesTunisia
  3. 3.Département de MathématiquesFaculté des sciences de SfaxSfaxTunisia

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