The Quantum Gromov-Hausdorff Propinquity
classification
🧮 math.OA
math.FA
keywords
distancegromov-hausdorffquantumleibnizpropinquityrieffeladaptedalgebras
read the original abstract
We introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum compact metric spaces, which extends the Gromov-Hausdorff distance to noncommutative geometry and strengthens Rieffel's quantum Gromov-Hausdorff distance and Rieffel's proximity by making *-isomorphism a necessary condition for distance zero, while being well adapted to Leibniz seminorms. This work offers a natural solution to the long-standing problem of finding a framework for the development of a theory of Leibniz Lip-norms over C*-algebras.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
Quantum metrics from the trace on full matrix algebras
Certain natural quantum metrics on matrix algebras M_n are separated by positive Gromov-Hausdorff propinquity distance when n is not prime.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.