Approximation of quantum tori by finite quantum tori for the quantum Gromov--Hausdorff distance

DOI10.1016/j.jfa.2005.01.003zbMath1088.46044arXivmath/0310214OpenAlexW2116657894MaRDI QIDQ2484454

Frédéric Latrémolière

Publication date: 1 August 2005

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310214

zbMATH Keywords

quantum torusnoncommutative metric geometryquantum Gromov--Hausdorff distance

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Noncommutative geometry (à la Connes) (58B34)

Related Items (25)

The quantum Gromov-Hausdorff propinquity ⋮ Equivalence of quantum metrics with a common domain ⋮ Polynomial approximation of quantum Lipschitz functions ⋮ The Podleś spheres converge to the sphere ⋮ Curved noncommutative tori as Leibniz quantum compact metric spaces ⋮ A note on the perturbations of compact quantum metric spaces ⋮ Harmonic analysis approach to Gromov-Hausdorff convergence for noncommutative tori ⋮ The Gromov-Hausdorff propinquity for metric spectral triples ⋮ Convergence of inductive sequences of spectral triples for the spectral propinquity ⋮ Noncommutative solenoids and the Gromov-Hausdorff propinquity ⋮ Quantum Metric Spaces and the Gromov-Hausdorff Propinquity ⋮ Metrics and causality on Moyal planes ⋮ Some applications of conditional expectations to convergence for the quantum Gromov–Hausdorff propinquity ⋮ The dual Gromov-Hausdorff propinquity ⋮ Quantum (non-commutative) toric geometry: foundations ⋮ Convergence of spectral triples on fuzzy tori to spectral triples on quantum tori ⋮ Heat equation in a model matrix geometry ⋮ Quantum ultrametrics on AF algebras and the Gromov–Hausdorff propinquity ⋮ Spectral continuity for aperiodic quantum systems I. General theory ⋮ Extensions and degenerations of spectral triples ⋮ The modular Gromov–Hausdorff propinquity ⋮ The dual modular Gromov-Hausdorff propinquity and completeness ⋮ Bunce-Deddens algebras as quantum Gromov-Hausdorff distance limits of circle algebras ⋮ Sampling and periodization of generators of Heisenberg modules ⋮ Dynamics of compact quantum metric spaces

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