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A Characterization of Invariant Connections
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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A Characterization of Invariant Connections
Інший ID:
2010 Mathematics Subject Classification: 22F50; 53C05; 53C80; 83C45
DOI:10.3842/SIGMA.2014.025
DOI:10.3842/SIGMA.2014.025
Посилання:
A Characterization of Invariant Connections / M. Hanusch // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 10 назв. — англ.
Підтримка:
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.
Дата:
2014
Переглядів:
675
Завантажень:
259
Анотація:
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.
