Nontrivial Deformation of a Trivial Bundle
The SU(2)-prolongation of the Hopf fibration S³→S² is a trivializable principal SU(2)-bundle. We present a noncommutative deformation of this bundle to a quantum principal SUq(2)-bundle that is not trivializable. On the other hand, we show that the SUq(2)-bundle is piecewise trivializable with respe...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146823 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Nontrivial Deformation of a Trivial Bundle / P.M. Hajac, B. Zieliński // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862714731053187072 |
|---|---|
| author | Hajac, P.M. Zieliński, B. |
| author_facet | Hajac, P.M. Zieliński, B. |
| citation_txt | Nontrivial Deformation of a Trivial Bundle / P.M. Hajac, B. Zieliński // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The SU(2)-prolongation of the Hopf fibration S³→S² is a trivializable principal SU(2)-bundle. We present a noncommutative deformation of this bundle to a quantum principal SUq(2)-bundle that is not trivializable. On the other hand, we show that the SUq(2)-bundle is piecewise trivializable with respect to the closed covering of S² by two hemispheres intersecting at the equator.
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| first_indexed | 2025-12-07T17:53:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146823 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:53:37Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hajac, P.M. Zieliński, B. 2019-02-11T16:33:28Z 2019-02-11T16:33:28Z 2014 Nontrivial Deformation of a Trivial Bundle / P.M. Hajac, B. Zieliński // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 14 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58B32 DOI:10.3842/SIGMA.2014.031 https://nasplib.isofts.kiev.ua/handle/123456789/146823 The SU(2)-prolongation of the Hopf fibration S³→S² is a trivializable principal SU(2)-bundle. We present a noncommutative deformation of this bundle to a quantum principal SUq(2)-bundle that is not trivializable. On the other hand, we show that the SUq(2)-bundle is piecewise trivializable with respect to the closed covering of S² by two hemispheres intersecting at the equator. This paper is a contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in
 honor of Marc A. Rief fel. The full collection is available at http://www.emis.de/journals/SIGMA/Rieffel.html.
 The authors are grateful to Tomasz Brzezi´nski for discussions, and to the referees for careful
 proofreading of the manuscript. This work was partially supported by the NCN-grant
 2011/01/B/ST1/06474. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nontrivial Deformation of a Trivial Bundle Article published earlier |
| spellingShingle | Nontrivial Deformation of a Trivial Bundle Hajac, P.M. Zieliński, B. |
| title | Nontrivial Deformation of a Trivial Bundle |
| title_full | Nontrivial Deformation of a Trivial Bundle |
| title_fullStr | Nontrivial Deformation of a Trivial Bundle |
| title_full_unstemmed | Nontrivial Deformation of a Trivial Bundle |
| title_short | Nontrivial Deformation of a Trivial Bundle |
| title_sort | nontrivial deformation of a trivial bundle |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146823 |
| work_keys_str_mv | AT hajacpm nontrivialdeformationofatrivialbundle AT zielinskib nontrivialdeformationofatrivialbundle |