Smooth Lie group actions are parametrized diffeological subgroups

Patrick Iglesias-Zemmour (1) , Yael Karshon (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 Department of Mathematics [University of Toronto]

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 Diff(M), where the image is equipped with the subset diffeology of the functional diffeology.

Mots clés: diffeology; Lie group; diffeomorphism

Domaines: Géométrie différentielle [math.DG]; Géométrie symplectique [math.SG]

Patrick Iglesias-Zemmour, Yael Karshon. Smooth Lie group actions are parametrized diffeological subgroups. Proceedings of the American Mathematical Society, 2012, 140 (2), pp.731-739. ⟨10.1090/S0002-9939-2011-11301-7⟩. ⟨hal-01288464⟩