The Quantum Metric Structure of Quantum SU(2)
We introduce a two parameter family of Dirac operators on quantum SU(2) and analyse their properties from the point of view of non-commutative metric geometry. It is shown that these Dirac operators give rise to compact quantum metric structures, and that the corresponding two parameter family of co...
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European Mathematical Society Publishing House
2025
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=4154975&site=ehost-live header: @attributes: shortDbName: nlebk uiTerm: 4154975 longDbName: eBook Collection (EBSCOhost) uiTag: AN controlInfo: bkinfo: btl: The Quantum Metric Structure of Quantum SU(2) aug: au: Jens Kaad, David Kyed sertl: Memoirs of the European Mathematical Society isbn: 9783985470914 9783985475919 imageinfo: pubinfo: dt: @attributes: year: 2025 month: 01 day: 01 dtAvail: @attributes: year: 2025 month: 09 day: 04 vid: 00018 pub: European Mathematical Society Publishing House pubContract: European Mathematical Society - EMS - Publishing House GmbH place: Berlin price: 0.01 limitsGroup: maxCheckoutDays: 1500 pda: N printPagesOffline: 100 printPagesOnline: 100 previewPages: 10000 prePubGroup: dewey: @attributes: class: 512.55 item: 512 .55 lc: @attributes: class: QC174.17.G7 K33 2025eb item: QC 174 .17 .G7 K33 2025eb artinfo: ui: 4154975 1519270973 formats: fmt: @attributes: type: EB doid: NL$4154975$PDF caption: PDF download: Y tig: atl: The Quantum Metric Structure of Quantum SU(2) ptl: The Quantum Metric Structure of Quantum SU(2) aug: au: Jens Kaad, David Kyed su: Geometric quantization Quantum groups sug: subj: MATHEMATICS / Matrices Geometric quantization Quantum groups ab: We introduce a two parameter family of Dirac operators on quantum SU(2) and analyse their properties from the point of view of non-commutative metric geometry. It is shown that these Dirac operators give rise to compact quantum metric structures, and that the corresponding two parameter family of compact quantum metric spaces varies continuously in Rieffel's quantum Gromov–Hausdorff distance. This continuity result includes the classical case where we recover the round 3-sphere up to a global scaling factor on the metric. Our main technical tool is a quantum SU(2) analogue of the Berezin transform, together with its associated fuzzy approximations, the analysis of which also leads to a systematic way of approximating Lipschitz operators by means of polynomial expressions in the generators. pubtype: eBook doctype: Book ougenre: Book language: English copyright: @attributes: flag: N copyrightText: holdings: @attributes: islocal: N |
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