C*-algebraic quantum Gromov-Hausdorff distance

2003/11/28 by Hanfeng Li, Li, Hanfeng · 1 citation
Mathematics · #58B34 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Primary 46L87 #Quantum Algebra (math.QA) #Secondary 53C23 #math.OA #math.QA #msc:46L87 #msc:53C23 #msc:58B34

paper · pdf · doi:10.48550/arxiv.math/0312003

27 pages. Small modifications

openalex publication_date 2003/11/28 · arxiv created 2004/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new quantum Gromov-Hausdorff distance between C*-algebraic compact quantum metric spaces. Because it is able to distinguish algebraic structures, this new distance fixes a weakness of Rieffel's quantum distance. We show that this new quantum distance has properties analogous to the basic properties of the classical Gromov-Hausdorff distance, and we give criteria for when a parameterized family of C*-algebraic compact quantum metric spaces is continuous with respect to this new distance.

Citations

• Embedding of exact C*-algebras and continuous fields in the Cuntz algebra O₂

Cited by

• Quantum Metric Structures on Iwahori-Hecke Algebras

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