Skip to main content
SpringerLink
Log in

Equivalence of deformations and associated *-products

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

In this letter we study the non-trivial formal differentiable deformations of the Lie algebraN=C ∞(W, IR) whereW is a symplectic manifold. Under some assumptions (satisfied in particular forW=IR2n) we show that these deformations are all equivalent, up to a monomial change of the parameter, to one of them (Moyal for IR2n). Furthermore, if there exists a differentiable *-product corresponding to one of them, each of them is induced by a *-product which is essentially unique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. AvezA., LichnerowiczA., and Diaz-MirandaA.,J. Differential Geometry 9, 1 (1974).

    Google Scholar 

  2. BayenF., FlatoM., FronsdalC., LichnerowiczA., and SternheimerD., ‘Deformation of symplectic structures’,Ann. Phys. 111, 61 (1978).

    Google Scholar 

  3. BayenF., FlatoM., FronsdalC., LichnerowiczA., and SternheimerD., ‘Deformation theory and quantization’,Ann. Phys. 111, 111 (1978).

    Google Scholar 

  4. Lichnerowicz, A., (to be published).

  5. MoyalJ.E.,Proc. Cambridge Phil. Soc. 45, 99 (1949).

    Google Scholar 

  6. VeyJ.,Comment. Math. Helvet. 50, 421 (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. U.L.B. Campus Plaine, C.P. 218 Bd. du Triomphe, B-1050, Bruxelles, Belgium

    Simone Gutt

Authors
  1. Simone Gutt
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Aspirant du Fonds National belge de la Recherche Scientifique.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gutt, S. Equivalence of deformations and associated *-products. Lett Math Phys 3, 297–309 (1979). https://doi.org/10.1007/BF01821850

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01821850

Keywords

Search

Navigation