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 |
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| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-146823 |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Nontrivial Deformation of a Trivial Bundle |
| spellingShingle |
Nontrivial Deformation of a Trivial Bundle Hajac, P.M. Zieliński, B. |
| title_short |
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_sort |
nontrivial deformation of a trivial bundle |
| author |
Hajac, P.M. Zieliński, B. |
| author_facet |
Hajac, P.M. Zieliński, B. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146823 |
| 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. |
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AT hajacpm nontrivialdeformationofatrivialbundle AT zielinskib nontrivialdeformationofatrivialbundle |
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2025-12-07T17:53:37Z |
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2025-12-07T17:53:37Z |
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1850872973247905793 |