A Characterization of Invariant Connections
Given a principal fibre bundle with structure group S, and a fibre transitive Lie group G of automorphisms thereon, Wang's theorem identifies the invariant connections with certain linear maps ψ:g→s. In the present paper, we prove an extension of this theorem which applies to the general situat...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2014 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146822 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Characterization of Invariant Connections / M. Hanusch // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862672772565565440 |
|---|---|
| author | Hanusch, M. |
| author_facet | Hanusch, M. |
| citation_txt | A Characterization of Invariant Connections / M. Hanusch // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Given a principal fibre bundle with structure group S, and a fibre transitive Lie group G of automorphisms thereon, Wang's theorem identifies the invariant connections with certain linear maps ψ:g→s. In the present paper, we prove an extension of this theorem which applies to the general situation where G acts non-transitively on the base manifold. We consider several special cases of the general theorem, including the result of Harnad, Shnider and Vinet which applies to the situation where G admits only one orbit type. Along the way, we give applications to loop quantum gravity.
|
| first_indexed | 2025-12-07T15:36:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146822 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:36:46Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hanusch, M. 2019-02-11T16:32:30Z 2019-02-11T16:32:30Z 2014 A Characterization of Invariant Connections / M. Hanusch // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 10 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 22F50; 53C05; 53C80; 83C45 DOI:10.3842/SIGMA.2014.025 https://nasplib.isofts.kiev.ua/handle/123456789/146822 Given a principal fibre bundle with structure group S, and a fibre transitive Lie group G of automorphisms thereon, Wang's theorem identifies the invariant connections with certain linear maps ψ:g→s. In the present paper, we prove an extension of this theorem which applies to the general situation where G acts non-transitively on the base manifold. We consider several special cases of the general theorem, including the result of Harnad, Shnider and Vinet which applies to the situation where G admits only one orbit type. Along the way, we give applications to loop quantum gravity. The author is grateful to the anonymous referees for several helpful comments and suggestions.
 Moreover, he thanks Christian Fleischhack for numerous discussions and many helpful comments
 on a draft of the present article. He is grateful for discussion with various members of the math
 faculty of the University of Paderborn. In particular, with Joachim Hilgert, Bernhard Krotz,
 Benjamin Schwarz and Andreas Schmied. He also thanks Gerd Rudolph for general discussions
 and comments on a first draft of this article. The author has been supported by the EmmyNoether-Programm
 of the Deutsche Forschungsgemeinschaft under grant FL 622/1-1. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Characterization of Invariant Connections Article published earlier |
| spellingShingle | A Characterization of Invariant Connections Hanusch, M. |
| title | A Characterization of Invariant Connections |
| title_full | A Characterization of Invariant Connections |
| title_fullStr | A Characterization of Invariant Connections |
| title_full_unstemmed | A Characterization of Invariant Connections |
| title_short | A Characterization of Invariant Connections |
| title_sort | characterization of invariant connections |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146822 |
| work_keys_str_mv | AT hanuschm acharacterizationofinvariantconnections AT hanuschm characterizationofinvariantconnections |