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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2014 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.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| Резюме: | 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.
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| ISSN: | 1815-0659 |