Gromov-Hausdorff convergence of quantised intervals

David Kyed*, Jens Kaad, Thomas Gotfredsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The Podleś quantum sphere S q 2 admits a natural commutative C -subalgebra I q with spectrum {0}∪{q 2k:k∈N 0}, which may therefore be considered as a quantised version of a classical interval. We study here the compact quantum metric space structure on I q inherited from the corresponding structure on S q 2, and provide an explicit formula for the metric induced on the spectrum. Moreover, we show that the resulting metric spaces vary continuously in the deformation parameter q with respect to the Gromov-Hausdorff distance, and that they converge to a classical interval of length π as q tends to 1.

Translated title of the contributionGromov-Hausdorff convergence of quantised intervals
Original languageEnglish
Article number125131
JournalJournal of Mathematical Analysis and Applications
Volume500
Issue number2
Number of pages13
ISSN0022-247X
DOIs
Publication statusPublished - 15. Aug 2021

Keywords

  • Gromov-Hausdorff distance
  • Podleś sphere
  • Quantum metric spaces

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