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:
| Дата: | 2014 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146822 |
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| 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| id |
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irk-123456789-1468222019-02-12T01:25:09Z A Characterization of Invariant Connections Hanusch, M. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146822 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Hanusch, M. |
| spellingShingle |
Hanusch, M. A Characterization of Invariant Connections Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Hanusch, M. |
| author_sort |
Hanusch, M. |
| title |
A Characterization of Invariant Connections |
| title_short |
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_sort |
characterization of invariant connections |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146822 |
| citation_txt |
A Characterization of Invariant Connections / M. Hanusch // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 10 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT hanuschm acharacterizationofinvariantconnections AT hanuschm characterizationofinvariantconnections |
| first_indexed |
2023-05-20T17:25:43Z |
| last_indexed |
2023-05-20T17:25:43Z |
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1796153270398353408 |