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Letters in Mathematical Physics

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

Discrete Heisenberg-Weyl Group and modular group

  • L. D. Faddeev
Article

Abstract

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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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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