The Podleś Spheres Converge to the Sphere

Konrad Aguilar; Jens Kaad; David Kyed

doi:10.1007/s00220-022-04363-4

The Podleś Spheres Converge to the Sphere

Konrad Aguilar, Jens Kaad^*, David Kyed

^*Kontaktforfatter

Pomona College

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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Abstract

We prove that the Podleś spheres S²_q 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 S²_q as their linear dimension tends to infinity, thus providing a quantum counterpart to a classical result of Rieffel.

Originalsprog	Engelsk
Tidsskrift	Communications in Mathematical Physics
Vol/bind	392
Udgave nummer	3
Sider (fra-til)	1029-1061
ISSN	0010-3616
DOI	https://doi.org/10.1007/s00220-022-04363-4
Status	Udgivet - jun. 2022

Bibliografisk 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.

Dokumenter og links

10.1007/s00220-022-04363-4

Open access versionAccepteret manuskript, 559 KB

https://arxiv.org/pdf/2102.12761

SDU link

Tjek adgangen til materialet i Syddansk Universitetsbiblioteks søgemaskine

Citationsformater

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AU - Kaad, Jens

AU - Kyed, David

N1 - 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.

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N2 - 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.

AB - 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.

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The Podleś Spheres Converge to the Sphere

Abstract

Bibliografisk note

Dokumenter og links

SDU link

Fingeraftryk

Citationsformater