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arXiv · 2007.09694

Gromov-Hausdorff convergence of quantised intervals

Thomas Gotfredsen·Jens Kaad·David Kyed
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Abstract

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.

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Thomas Gotfredsen, Jens Kaad, David Kyed. 2020-07-19. Gromov-Hausdorff convergence of quantised intervals. https://arxiv.org/abs/2007.09694

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