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Completing Lie algebra actions to Lie group actions

Franz W. Kamber·Peter W. Michor
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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 $T_1$ 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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Franz W. Kamber, Peter W. Michor. 2003-10-20. Completing Lie algebra actions to Lie group actions. https://arxiv.org/abs/math/0310308

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