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On the Relationship between Classical and Deformed Hopf Fibrations

Tomasz Brzezinski Orcid Logo, James Gaunt, Alexander Schenkel

Symmetry, Integrability and Geometry: Methods and Applications, Volume: 16, Issue: 008

Swansea University Author: Tomasz Brzezinski Orcid Logo

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DOI (Published version): 10.3842/sigma.2020.008

Abstract

The θ-deformed Hopf fibration S3θ → S2 over the commutative 2-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of classical and deformed connections are isomorphic. T...

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Published in: Symmetry, Integrability and Geometry: Methods and Applications
ISSN: 1815-0659
Published: SIGMA (Symmetry, Integrability and Geometry: Methods and Application) 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa53623
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first_indexed 2020-02-24T13:40:17Z
last_indexed 2020-10-24T03:06:02Z
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spelling 2020-10-23T11:26:21.9968195 v2 53623 2020-02-24 On the Relationship between Classical and Deformed Hopf Fibrations 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2020-02-24 SMA The θ-deformed Hopf fibration S3θ → S2 over the commutative 2-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of classical and deformed connections are isomorphic. The latter isomorphism is equivariant under an appropriate notion of infinitesimal gauge transformations in these contexts. Gauge transformations and connections on associated modules are studied and are shown to be sensitive to the deformation parameter. A homotopy theoretic explanation for the existence of a close relationship between the classical and deformed Hopf fibrations is proposed. Journal Article Symmetry, Integrability and Geometry: Methods and Applications 16 008 SIGMA (Symmetry, Integrability and Geometry: Methods and Application) 1815-0659 noncommutative geometry; principal comodule algebras; noncommutative principal bundles; Hopf fibrations; homotopy equivalence 23 2 2020 2020-02-23 10.3842/sigma.2020.008 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2020-10-23T11:26:21.9968195 2020-02-24T11:25:28.7048859 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Tomasz Brzezinski 0000-0001-6270-3439 1 James Gaunt 2 Alexander Schenkel 3 53623__16672__2978b09dcfbd4e568626fcbdf9a4320c.pdf sigma20-008.pdf 2020-02-24T11:58:20.6204918 Output 603185 application/pdf Version of Record true true eng
title On the Relationship between Classical and Deformed Hopf Fibrations
spellingShingle On the Relationship between Classical and Deformed Hopf Fibrations
Tomasz Brzezinski
title_short On the Relationship between Classical and Deformed Hopf Fibrations
title_full On the Relationship between Classical and Deformed Hopf Fibrations
title_fullStr On the Relationship between Classical and Deformed Hopf Fibrations
title_full_unstemmed On the Relationship between Classical and Deformed Hopf Fibrations
title_sort On the Relationship between Classical and Deformed Hopf Fibrations
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Tomasz Brzezinski
James Gaunt
Alexander Schenkel
format Journal article
container_title Symmetry, Integrability and Geometry: Methods and Applications
container_volume 16
container_issue 008
publishDate 2020
institution Swansea University
issn 1815-0659
doi_str_mv 10.3842/sigma.2020.008
publisher SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
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description The θ-deformed Hopf fibration S3θ → S2 over the commutative 2-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of classical and deformed connections are isomorphic. The latter isomorphism is equivariant under an appropriate notion of infinitesimal gauge transformations in these contexts. Gauge transformations and connections on associated modules are studied and are shown to be sensitive to the deformation parameter. A homotopy theoretic explanation for the existence of a close relationship between the classical and deformed Hopf fibrations is proposed.
published_date 2020-02-23T04:06:40Z
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score 11.037144

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