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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Infinitesimal characterization of homogeneous bundles


Author: Kirill Mackenzie
Journal: Proc. Amer. Math. Soc. 103 (1988), 1271-1277
MSC: Primary 55R20; Secondary 53C05, 53C10, 57R22
MathSciNet review: 955021
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Abstract: Consider a principal bundle $ Q(B,H)$ on a base $ B$ which is compact and has finite fundamental group. We give necessary and sufficient conditions, in terms of the Atiyah sequence of $ Q(B,H)$, for $ Q(B,H)$ to be locally isomorphic to a bundle of the form $ G(G/S,S)$ for $ G$ a Lie group and $ S$ a closed subgroup of $ G$. The proof involves the careful integration of certain infinitesimal actions of a Lie algebra on $ Q,B$ and the universal cover of $ B$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0955021-1
PII: S 0002-9939(1988)0955021-1
Article copyright: © Copyright 1988 American Mathematical Society