Completing Lie algebra actions to Lie group actions

2003/10/20 by Franz W. Kamber, Peter W. Michor · 1 citation
Mathematics · #math.DG #msc:22F05 #msc:37C10 #msc:54H15 #msc:57R30 #msc:57S05 #msc:58A40

paper · pdf

published as Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 1-10 · 10 pages, Latex

arxiv created 2003/10/20 · arxiv updated 2009/12/01

Abstract

For a finite dimensional Lie algebra \g of vector fields on a manifold M we show that M can be completed to a G-space in a unversal way, which however is neither Hausdorff nor T₁ in general. Here G is a connected Lie group with Lie-algebra \g. For a transitive \g-action the completion is of the form G/H for a Lie subgroup H which need not be closed. In general the completion can be constructed by completing each \g-orbit.

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