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 onL 2(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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Schwinger, J.:Proc. Nat. Acad. Sci. USA 46 (1960), 1401.
Faddeev, L. and Volkov, A.:Phys. Lett. B 315 (1993), 311.
Faddeev, L.: Lectures delivered at the International School of Physics ‘Enrico Fermi’ Varenna, Italy, 1994, hep-th/9408041.
Connes, A.:Non-commutative Geometry: Academic Press, New York, 1994.
Polyakov, A.:Gauge Fields and Strings, Ellis Harwood, Chichester, 1991.
Faddeev, L.:Lett. ZhETP 21 (1975), 141.
Rieffel, M. A.,Pacific J. Math. 93 (1981), 715.