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arXiv · 2112.11299

Smooth actions of connected compact Lie groups with a free point are determined by two vector fields

F. J. Turiel·A. Viruel
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Abstract

Consider a smooth action $\mathbf G\times M \rightarrow M$ of a compact connected Lie group $\mathbf G$ on a connected manifold $M$. Assume the existence of a point of $M$ whose isotropy group has a single element (free point). Then we prove that there exist two complete vector field $X,X_1$ such that their group of automorphisms equals $\mathbf G$ regarded as a group of diffeomorphisms of $M$ (the existence of a free point implies that the action of $\mathbf G$ is effective). Moreover, some examples of effective actions with no free point where this result fails are exhibited.

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F. J. Turiel, A. Viruel. 2021-12-21. Smooth actions of connected compact Lie groups with a free point are determined by two vector fields. https://doi.org/10.1016/j.geomphys.2024.105196

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