Convergence of Fuzzy Tori and Quantum Tori for the Quantum Gromov-Hausdorff Propinquity: An Explicit Approach

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Noncommutative metric geometry, Quantum Gromov-Hausdorff distance, Monge-Kantorovich distance, Quantum Metric Spaces, Lip-norms, Compact C*-metric spaces, Leibniz seminorms, Quantum Tori, Finite dimensional approximations.


Quantum tori are limits of finite dimensional C*-algebras for the quantum Gromov-Hausdorff propinquity, a metric defined by the author as a strengthening of Rieffel’s quantum Gromov-Hausdorff designed to retain the C*-algebraic structure. In this paper, we propose a proof of the continuity of the family of quantum and fuzzy tori which relies on explicit representations of the C*-algebras rather than on more abstract arguments, in a manner which takes full advantage of the notion of bridge defining the quantum propinquity.

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