Abstract
We provide a detailed study of actions of the integers on compact quantum metric spaces, which includes general criteria ensuring that the associated crossed product algebra is again a compact quantum metric space in a natural way. Moreover, we provide a flexible set of assumptions ensuring that a continuous family of-Automorphisms of a compact quantum metric space yields a field of crossed product algebras which varies continuously in Rieffel's quantum Gromov-Hausdorff distance. Finally, we show how our results apply to continuous families of Lip-isometric actions on compact quantum metric spaces and to families of diffeomorphisms of compact Riemannian manifolds which vary continuously in the Whitney-Topology.
Original language | English |
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Journal | Ergodic Theory and Dynamical Systems |
Volume | 41 |
Issue number | 7 |
Pages (from-to) | 2069-2109 |
ISSN | 0143-3857 |
DOIs | |
Publication status | Published - Jul 2021 |
Keywords
- 2020 Mathematics Subject Classification
- 46L05
- 46L89
- 47L65
- dynamics of Riemannian manifolds
- quantum metric spaces
- crossed products