Vol. 12, No. 2, 2019

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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 × 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