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

^*Corresponding author for this work

Pomona College

Research output: Contribution to journal › Journal article › Research › 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.

Original language	English
Journal	Communications in Mathematical Physics
Volume	392
Issue number	3
Pages (from-to)	1029-1061
ISSN	0010-3616
DOIs	https://doi.org/10.1007/s00220-022-04363-4
Publication status	Published - Jun 2022

Bibliographical 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.

Keywords

math.OA
math.FA
58B32, 58B34, 46L89, 46L30, 81R15, 81R60

Documents & Links

10.1007/s00220-022-04363-4

Open access versionAccepted manuscript, 559 KB

https://arxiv.org/pdf/2102.12761

Cite this

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title = "The Podle{\'s} Spheres Converge to the Sphere",

abstract = "We prove that the Podle{\'s} 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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author = "Konrad Aguilar and Jens Kaad and David Kyed",

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. ",

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T1 - The Podleś Spheres Converge to the Sphere

AU - Aguilar, Konrad

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.

PY - 2022/6

Y1 - 2022/6

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.

KW - math.OA

KW - math.FA

KW - 58B32, 58B34, 46L89, 46L30, 81R15, 81R60

U2 - 10.1007/s00220-022-04363-4

DO - 10.1007/s00220-022-04363-4

M3 - Journal article

SN - 0010-3616

VL - 392

SP - 1029

EP - 1061

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

The Podleś Spheres Converge to the Sphere

Abstract

Bibliographical note

Keywords

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