Quantum metrics from traces on full matrix algebras

Aguilar, Konrad; Brooker, Samantha

doi:10.2140/involve.2019.12.329

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Quantum metrics from traces on full matrix algebras

Konrad Aguilar and Samantha Brooker

Vol. 12 (2019), No. 2, 329–342

DOI: 10.2140/involve.2019.12.329

Abstract

We prove that, in the sense of the Gromov–Hausdorff propinquity, certain natural quantum metrics on the algebras of $(n \times n)$ -matrices are separated by a positive distance when $n$ is not prime.

Keywords

noncommutative metric geometry, Gromov–Hausdorff propinquity, quantum metric spaces, Lip-norms, C*-algebras, full matrix algebras

Mathematical Subject Classification 2010

Primary: 46L89, 46L30, 58B34

Milestones

Received: 5 December 2017

Accepted: 7 March 2018

Published: 8 October 2018

Communicated by David Royal Larson

Authors

Konrad Aguilar
School of Mathematical and Statistical Sciences Arizona State University Tempe, AZ United States

Samantha Brooker
Department of Mathematics University of Denver Denver, CO United States

Vol. 12, No. 2, 2019