Dynamics of compact quantum metric spaces
arXiv:1904.13278 · doi:10.1017/etds.2020.34
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. We moreover 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. Lastly 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 C^1-topology.
v2: minor changes; to appear in Ergodic Theory and Dynamical Systems
References in corpus (14)
- Gravity coupled with matter and foundation of non-commutative geometry
- Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
- Metrics on State Spaces
- Metrics on states from actions of compact groups
- Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples
- Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance
- Type III and spectral triples
- Nonunital spectral triples and metric completeness in unbounded KK-theory
- Dynamical Systems on Spectral Metric Spaces
- Local index formula and twisted spectral triples
- theta-deformations as compact quantum metric spaces
- Noncommutative Geometry and Conformal Geometry. I. Local Index Formula and Conformal Invariants
- Untwisting twisted spectral triples
- A residue formula for the fundamental Hochschild 3-cocycle for SUq(2)