Structure groups and holonomy in infinite dimensions |
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Authors: | Jean-Pierre Magnot |
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Institution: | Institut für Angewandte Mathematik, Abt. f. Wahrscheinlichkeitstheorie und Mathematische Statistik, Wegelerstr. 6, 53115 Bonn, Germany |
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Abstract: | We give a theorem of reduction of the structure group of a principal bundle P with regular structure group G. Then, when G is in the classes of regular Lie groups defined by T. Robart in Can. J. Math. 49 (4) (1997) 820-839], we define the closed holonomy group of a connection as the minimal closed Lie subgroup of G for which the previous theorem of reduction can be applied. We also prove an infinite dimensional version of the Ambrose-Singer theorem: the Lie algebra of the holonomy group is spanned by the curvature elements. |
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Keywords: | 58B99 53C29 |
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