Discrete Heisenberg-Weyl Group and modular group
Copyright policy )Discrete Heisenberg-Weyl Group and modular group
It is shown that the generators of two discrete Heisenberg-Weyl groups with irrational rotation numbers $��$ and $-1/ ��$ generate the whole algebra $\cal B$ of bounded operators on $L_2(\bf R)$. The natural action of the modular group in $\cal B$ is implied. Applications to dynamical algebras appearing in lattice regularization and some duality principles are discussed.
12 pages, LaTeX file
- Department of Mathematical Sciences Russian Federation
- University of Helsinki Finland
- Steklov Mathematical Institute Russian Federation
Functional calculus for linear operators, High Energy Physics - Theory, discrete Heisenberg-Weyl groups with irrational rotation numbers, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, modular group, FOS: Physical sciences, Commutation relations and statistics as related to quantum mechanics (general), High Energy Physics - Theory (hep-th), lattice regularization, dynamical algebras, generators, Representation theory of linear operators
Functional calculus for linear operators, High Energy Physics - Theory, discrete Heisenberg-Weyl groups with irrational rotation numbers, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, modular group, FOS: Physical sciences, Commutation relations and statistics as related to quantum mechanics (general), High Energy Physics - Theory (hep-th), lattice regularization, dynamical algebras, generators, Representation theory of linear operators
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