The Podleś Spheres Converge to the Sphere

Konrad Aguilar, Jens Kaad*, David Kyed

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

We prove that the Podleś spheres S2q converge in quantum Gromov–Hausdorff distance to the classical 2-sphere as the deformation parameter q tends to 1. Moreover, we construct a q-deformed analogue of the fuzzy spheres, and prove that they converge to S2q as their linear dimension tends to infinity, thus providing a quantum counterpart to a classical result of Rieffel.

Original languageEnglish
JournalCommunications in Mathematical Physics
Volume392
Issue number3
Pages (from-to)1029-1061
ISSN0010-3616
DOIs
Publication statusPublished - Jun 2022

Bibliographical note

Funding Information:
The authors gratefully acknowledge the financial support from the Independent Research Fund Denmark through Grant Nos. 9040-00107B and 7014-00145B. Furthermore, they would like to thank Marc Rieffel for pointing out the reference [], and the anonymous referees for their careful reading of the manuscript.

Keywords

  • math.OA
  • math.FA
  • 58B32, 58B34, 46L89, 46L30, 81R15, 81R60

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