Gromov-Hausdorff convergence of quantised intervals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:500

Article

Gotfredsen, Thomas¹  Kaad, Jens¹  Kyed, David¹ 

[1] Univ Southern Denmark, Dept Math & Comp Sci, Campusvej 55, DK-5230 Odense M, Denmark

关键词: Quantum metric spaces;    Podles sphere;    Gromov-Hausdorff distance;   

DOI  :  10.1016/j.jmaa.2021.125131

来源: Elsevier

【 摘 要 】

The Podles quantum sphere S-q(2) admits a natural commutative C*-subalgebra I-q with spectrum {0} boolean OR {q(2k): k is an element of 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 qwith respect to the Gromov-Hausdorff distance, and that they converge to a classical interval of length pi as q tends to 1. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free