Faddeev, L. D. Discrete Heisenberg-Weyl group and modular group. (English) Zbl 0836.47012 Lett. Math. Phys. 34, No. 3, 249-254 (1995). Summary: It is shown that the generators of two discrete Heisenberg-Weyl groups with irrational rotation numbers \(\theta\) and \(-1/ \theta\) generate the whole algebra \({\mathcal B}\) of operators on \(L_2 (\mathbb{R})\). The natural action of the modular group in \({\mathcal B}\) is implied. Applications to dynamical algebras appearing in lattice regularization and some duality principles are discussed. Cited in 4 ReviewsCited in 143 Documents MSC: 47A60 Functional calculus for linear operators 47A67 Representation theory of linear operators 22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations 81S05 Commutation relations and statistics as related to quantum mechanics (general) Keywords:generators; discrete Heisenberg-Weyl groups with irrational rotation numbers; modular group; dynamical algebras; lattice regularization × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Schwinger, J.:Proc. Nat. Acad. Sci. USA 46 (1960), 1401. · Zbl 0125.21603 · doi:10.1073/pnas.46.10.1401 [2] Faddeev, L. and Volkov, A.:Phys. Lett. B 315 (1993), 311. · Zbl 0864.17042 · doi:10.1016/0370-2693(93)91618-W [3] Faddeev, L.: Lectures delivered at the International School of Physics ’Enrico Fermi’ Varenna, Italy, 1994, hep-th/9408041. [4] Connes, A.:Non-commutative Geometry: Academic Press, New York, 1994. · Zbl 0818.46076 [5] Polyakov, A.:Gauge Fields and Strings, Ellis Harwood, Chichester, 1991. · Zbl 1021.81879 [6] Faddeev, L.:Lett. ZhETP 21 (1975), 141. [7] Rieffel, M. A.,Pacific J. Math. 93 (1981), 715. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.