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Smooth Lie group actions are parametrized diffeological subgroups

Authors: Patrick Iglesias-Zemmour and Yael Karshon
Journal: Proc. Amer. Math. Soc. 140 (2012), 731-739
MSC (2010): Primary 58B25
Published electronically: September 21, 2011
MathSciNet review: 2846342
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that every effective smooth action of a Lie group $ G$ on a manifold $ M$ is a diffeomorphism from $ G$ onto its image in $ \mathrm{Diff}(M)$, where the image is equipped with the subset diffeology of the functional diffeology.

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Additional Information

Patrick Iglesias-Zemmour
Affiliation: Laboratoire d’Analyse, Topologie et Probabilités, CNRS, Marseille, France – and – The Hebrew University of Jerusalem, Israel

Yael Karshon
Affiliation: Department of Mathematics, The University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4, Canada

Received by editor(s): November 30, 2010
Published electronically: September 21, 2011
Additional Notes: This research is partially supported by an NSERC Discovery Grant.
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.