Metric Tannakian Duality

Details Metric Tannakian Duality Metric Tannakian Duality

2011-03-31

arxiv.org/abs/1104.0028v1

Mathematics

Quantum Algebra

Comments welcome. 11 pages

Scientific paper

We incorporate metric data into the framework of Tannaka-Krein duality. Thus, for any group with left invariant metric, we produce a dual metric on its category of unitary representations. We characterize the conditions under which a "double-dual" metric on the group may be recovered from the metric on representations, and provide conditions under which a metric agrees with its double-dual. We also consider some applications to T-duality and quantum Gromov-Hausdorff distance.

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