Gromov-Hausdorff convergence of quantised intervals

Bidragets oversatte titel: Gromov-Hausdorff convergence of quantised intervals

David Kyed*, Jens Kaad, Thomas Gotfredsen

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Abstrakt

The Podles quantum sphere S^2_q admits a natural commutative C*-subalgebra I_q with spectrum {0} \cup {q^{2k}: k = 0,1,2,...}, 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^2_q, 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 pi as q tends to 1.
Bidragets oversatte titelGromov-Hausdorff convergence of quantised intervals
OriginalsprogEngelsk
Artikelnummer125131
TidsskriftJournal of Mathematical Analysis and Applications
Vol/bind500
Udgave nummer2
Antal sider13
ISSN0022-247X
DOI
StatusUdgivet - 15. aug. 2021

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