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arXiv · 1708.01973

Actions of Categories by Lipschitz morphisms on limits for the Gromov-Hausdorff Propinquity

Frederic Latremoliere
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Abstract

We prove a compactness result for classes of actions of many small categories on quantum compact metric spaces by Lipschitz linear maps, for the topology of the covariant Gromov-Hausdorff propinquity. In particular, our result applies to actions of proper groups by Lipschitz isomorphisms on quantum compact spaces. Our result provides a first example of a structure which passes to the limit of quantum metric spaces for the propinquity, as well as a new method to construct group actions, including from non-locally compact groups seen as inductive limits of compact groups, on unital C*-algebras. We apply our techniques to obtain some properties of closure of certain classes of {\gQqcms s} for the propinquity.

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Frederic Latremoliere. 2017-08-07. Actions of Categories by Lipschitz morphisms on limits for the Gromov-Hausdorff Propinquity. https://arxiv.org/abs/1708.01973

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