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Heisenberg Modules over Quantum 2-tori are Metrized Quantum Vector Bundles

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Abstract The modular Gromov–Hausdorff propinquity is a distance on classes of modules endowed with quantum metric information, in the form of a metric form of a connection and a left… Click to show full abstract

Abstract The modular Gromov–Hausdorff propinquity is a distance on classes of modules endowed with quantum metric information, in the form of a metric form of a connection and a left Hilbert module structure. This paper proves that the family of Heisenberg modules over quantum two tori, when endowed with their canonical connections, form a family of metrized quantum vector bundles, as a first step in proving that Heisenberg modules form a continuous family for the modular Gromov–Hausdorff propinquity.

Keywords: modules quantum; quantum vector; heisenberg modules; metrized quantum; vector bundles

Journal Title: Canadian Journal of Mathematics
Year Published: 2019

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