Skip to main content
SpringerLink
Log in

The spectrum of the algebra of skew differential operators and the irreducible representations of the quantum Heisenberg algebra

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

Abstract

The left spectrum of a wide class of the algebras of skew differential operators is described. As a sequence, we determine and classify all the algebraically irreducible representations of the quantum Heisenberg algebra over an arbitrary field.

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

  • [C] Connes, A.: Géométrie Noncommutative. Paris: InterEditions 1990

    Google Scholar 

  • [D] Dixmier, J.: Algèbres Enveloppantes. Paris-Bruxelles-Montreal: Gauthier-Villars 1974

    Google Scholar 

  • [Dr] Drinfeld, V. G.: Quantum Groups. Proc. Int. Cong. Math., pp. 798–820. New York: Berkeley 1986

    Google Scholar 

  • [FG] Gelfand, I. M., Fairlie, D. B.: The Algebra of Weyl Symmetrized Polynomials and its Quantum Extension. Commun. Math. Phys.13 (1991)

  • [FK] Frenkel, I. B., Kac, V. G.: Basic Representations of Affine Lie Algebra and Dual Resonance Models, Invent. Math.62, 23–66 (1980)

    Google Scholar 

  • [FRT] Faddeev, L., Reshetikhin, N., Takhtajan, L.: Quantization of Lie Groups and Lie Algebras, preprint, LOMI-14-87; Algebra Analysis,1, no. 1 (1989)

  • [J] Jimbo, M.: Aq-Difference Analog ofU(g) and the Yang-Baxter Equation. Lett. Math. Phys.10, 63–69 (1985)

    Google Scholar 

  • [JG] Jaffe, A., Glimm, J.: Quantum Physics. Berlin, Heidelberg New York: Springer 1987

    Google Scholar 

  • [K] Kirillov, A.: Unitary representations of Unipotent Groups. Russ. Math. Surv.17, 57–110 (1962)

    Google Scholar 

  • [M] Manin, Yu. I.: Quantum Groups and Non-commutative Geometry, CRM, Université de Montréal (1988)

  • [R1] Rosenberg, A. L.: Noncommutative Affine Semischemes and Schemes, ‘Seminar on Supermanifolds,’ vol. 26, pp. 1–317, Report of Dept. of Math. of Stockholm University 1988

  • [R2] Rosenberg, A. L.: Left Spectrum, Levitzki Radical and Noncommutative Schemes, Proc. of Natl. Acad. vol.87, 1990

  • [S] Smith, S. P.: Quantum Groups: An Introduction and Survey for Ring Theorists, preprint

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics of Harvard University, 02138, Cambridge, MA, USA

    Alexander L. Rosenberg

Authors
  1. Alexander L. Rosenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by N. Yu. Reshetikhin

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rosenberg, A.L. The spectrum of the algebra of skew differential operators and the irreducible representations of the quantum Heisenberg algebra. Commun.Math. Phys. 142, 567–588 (1991). https://doi.org/10.1007/BF02099101

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02099101

Keywords

Search

Navigation