The Podles spheres converge to the sphere

Konrad Aguilar; Jens Kaad; David Kyed

The Podles spheres converge to the sphere

Konrad Aguilar, Jens Kaad, David Kyed

Department of Mathematics and Computer Science

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

We prove that the Podles spheres S²_p converge in quantum Gromov-Hausdorff distance to the classical 2-sphere as the deformation parameter _p 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	[to appear]
Number of pages	33
ISSN	0010-3616
Publication status	Accepted/In press - 2022

Keywords

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

Documents & Links

https://arxiv.org/pdf/2102.12761

Cite this

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title = "The Podles spheres converge to the sphere",

abstract = "We prove that the Podles spheres S2p converge in quantum Gromov-Hausdorff distance to the classical 2-sphere as the deformation parameter p 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.",

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

author = "Konrad Aguilar and Jens Kaad and David Kyed",

note = "33 pages",

year = "2022",

language = "English",

volume = "[to appear]",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Heinemann",

}

TY - JOUR

T1 - The Podles spheres converge to the sphere

AU - Aguilar, Konrad

AU - Kaad, Jens

AU - Kyed, David

N1 - 33 pages

PY - 2022

Y1 - 2022

N2 - We prove that the Podles spheres S2p converge in quantum Gromov-Hausdorff distance to the classical 2-sphere as the deformation parameter p 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 Podles spheres S2p converge in quantum Gromov-Hausdorff distance to the classical 2-sphere as the deformation parameter p 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

M3 - Journal article

VL - [to appear]

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -

The Podles spheres converge to the sphere

Abstract

Keywords

Documents & Links

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Cite this