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Mathematics > Operator Algebras

Title: Heisenberg Modules over Quantum 2-tori are metrized quantum vector bundles

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.
Comments: 38 Pages. Second part of arXiv:1608.04881v1; first part of arXiv:1703.07073v1; split due to length of paper
Subjects: Operator Algebras (math.OA)
MSC classes: 46L89
Cite as: arXiv:1703.07073 [math.OA]
  (or arXiv:1703.07073v3 [math.OA] for this version)

Submission history

From: Frederic Latremoliere [view email]
[v1] Tue, 21 Mar 2017 06:56:37 GMT (52kb)
[v2] Sun, 18 Feb 2018 04:08:56 GMT (52kb)
[v3] Sun, 18 Mar 2018 04:32:24 GMT (35kb)