Communications in Mathematical Physics

, Volume 169, Issue 3, pp 627–633 | Cite as

Deformation quantization of the Heisenberg group

  • F. Bonechi
  • R. Giachetti
  • E. Sorace
  • M. Tarlini


A *-product compatible with the comultiplication of the Hopf algebra of the functions on the Heisenberg group is determined by deforming a coboundary Lie-Poisson structure defined by a classicalr-matrix satisfying the modified Yang-Baxter equation. The corresponding quantum group is studied and itsR-matrix is explicitly calculated.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Vey, J.: Comment. Math. Helv.50, 421 (1975)Google Scholar
  2. 2.
    Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., Sternheimer, D.: Ann. Phys.110, 61 and 111 (1978)Google Scholar
  3. 3.
    Arnal, D.: Pacific J. Math.114, 285 (1984)Google Scholar
  4. 4.
    Rieffel, M.A.: Commun. Math. Phys.122, 531 (1989).Google Scholar
  5. 5.
    Rieffel, M.A.: American J. Math.112, 657 (1990)Google Scholar
  6. 6.
    Takhtajan, L.A.: Lectures on quantum groups. In: Introduction to quantum group and integrable massive models of quantum field theory. Nankai Lectures in Mathematical Physics. Singapore: World Scientific, 1990, p. 69Google Scholar
  7. 7.
    Drinfeld, V.G.: Sov. Math. Dokl.28, 667 (1983)Google Scholar
  8. 8.
    Ohn, Ch.: Lett. Math. Phys.25, 85 (1992)Google Scholar
  9. 9.
    Celeghini, E., Giachetti, R., Sorace, E., Tarlini, M.: J. Math. Phys.32, 1155 (1991)Google Scholar
  10. 10.
    Celeghini, E., Giachetti, R., Sorace, E., Tarlini, M.: Contractions of quantum groups. In: Lecture Notes in Mathematics 1510. Berlin, Heidelberg, New York: Springer 1992, p. 221Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • F. Bonechi
    • 1
  • R. Giachetti
    • 2
  • E. Sorace
    • 1
  • M. Tarlini
    • 1
  1. 1.Dipartimento di FisicaUniversità di Firenze and INFNFirenzeItaly
  2. 2.Dipartimento di MatematicaUniversità di BolognaBolognaItaly

Personalised recommendations