Letters in Mathematical Physics

, Volume 34, Issue 3, pp 249–254 | Cite as

Discrete Heisenberg-Weyl Group and modular group

  • L. D. Faddeev


It is shown that the generators of two discrete Heisenberg-Weyl groups with irrational rotation numbers θ and −1/θ generate the whole algebraB of operators onL2(R). The natural action of the modular group inB is implied. Applications to dynamical algebras appearing in lattice regularization and some duality principles are discussed.

Mathematics Subject Classification (1991)

47A60 47A67 22D25 


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  1. 1.
    Schwinger, J.:Proc. Nat. Acad. Sci. USA 46 (1960), 1401.ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Faddeev, L. and Volkov, A.:Phys. Lett. B 315 (1993), 311.ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Faddeev, L.: Lectures delivered at the International School of Physics ‘Enrico Fermi’ Varenna, Italy, 1994, hep-th/9408041.Google Scholar
  4. 4.
    Connes, A.:Non-commutative Geometry: Academic Press, New York, 1994.zbMATHGoogle Scholar
  5. 5.
    Polyakov, A.:Gauge Fields and Strings, Ellis Harwood, Chichester, 1991.Google Scholar
  6. 6.
    Faddeev, L.:Lett. ZhETP 21 (1975), 141.Google Scholar
  7. 7.
    Rieffel, M. A.,Pacific J. Math. 93 (1981), 715.MathSciNetCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • L. D. Faddeev
    • 1
    • 2
  1. 1.St. Petersburg Branch of Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.Research Institute for Theoretical PhysicsUniversity of HelsinkiHelsinkiFinland

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