Convergence of Fuzzy Tori and Quantum Tori for the Quantum Gromov-Hausdorff Propinquity: An Explicit Approach
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.
Latrémolière, F. (2013). Convergence of Fuzzy Tori and Quantum Tori for the Quantum Gromov-Hausdorff Propinquity: An explicit approach. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/17