Actions of categories by Lipschitz morphisms on limits for the Gromov–Hausdorff propinquity

  title={Actions of categories by Lipschitz morphisms on limits for the Gromov–Hausdorff propinquity},
  author={Fr{\'e}d{\'e}ric Latr{\'e}moli{\`e}re},
  journal={arXiv: Operator Algebras},
3 Citations
Convergence of Spectral Triples on Fuzzy Tori to Spectral Triples on Quantum Tori
Fuzzy tori are finite dimensional C*-algebras endowed with an appropriate notion of noncommutative geometry inherited from an ergodic action of a finite closed subgroup of the torus, which are meant


The covariant Gromov–Hausdorff propinquity
We extend the Gromov-Hausdorff propinquity to a metric on Lipschitz dynamical systems, which are given by strongly continuous actions of proper monoids on quantum compact metric spaces via Lipschitz
Bounded-Lipschitz Distances on the State Space of a C*-algebra
Metric noncommutative geometry, initiated by Alain Connes, has known some great recent developments under the impulsion of Rieffel and the introduction of the category of compact quantum metric
Quantum Ultrametrics on AF Algebras and The Gromov-Hausdorff Propinquity
We construct quantum metric structures on unital AF algebras with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite
Convergence of Cauchy sequences for the covariant Gromov–Hausdorff propinquity
Convergence of Fuzzy Tori and Quantum Tori for the Quantum Gromov-Hausdorff Propinquity: An Explicit Approach
Quantum tori are limits of finite dimensional C*-algebras for the quantum Gromov-Hausdorff propinquity, a metric defined by the author as a strengthening of Rieffel's quantum Gromov-Hausdorff
A Compactness Theorem for The Dual Gromov-Hausdorff Propinquity
We prove a compactness theorem for the dual Gromov-Hausdorff propinquity as a noncommutative analogue of the Gromov compactness theorem for the Gromov-Hausdorff distance. Our theorem is valid for
Triangle Inequality and the Dual Gromov-Hausdorff Propinquity
The dual Gromov-Hausdorff propinquity is a generalization of the Gromov-Hausdorff distance to the class of Leibniz quantum compact metric spaces, designed to be well-behaved with respect to