Geodesic
Completing Lie algebra actions to Lie group actions
Kamber, Franz1 ; Michor, Peter2
1 Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801
2 Institut für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria, and Erwin Schrödinger Institut für Mathematische Physik, Boltzmanngasse 9, A-1090 Wien, Austria
Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 1-10 Cet article a éte moissonné depuis la source American Mathematical Society

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For a finite-dimensional Lie algebra $\mathfrak {g}$ of vector fields on a manifold $M$ we show that $M$ can be completed to a $G$-space in a universal way, which however is neither Hausdorff nor $T_1$ in general. Here $G$ is a connected Lie group with Lie-algebra $\mathfrak {g}$. For a transitive $\mathfrak {g}$-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 $\mathfrak {g}$-orbit.
DOI : 10.1090/S1079-6762-04-00124-6

Kamber, Franz 1 ; Michor, Peter 2

1 Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801
2 Institut für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria, and Erwin Schrödinger Institut für Mathematische Physik, Boltzmanngasse 9, A-1090 Wien, Austria 
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Kamber, Franz; Michor, Peter. Completing Lie algebra actions to Lie group actions. Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 1-10. doi: 10.1090/S1079-6762-04-00124-6

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[2] Kamber, Franz W., Michor, Peter W. The flow completion of a manifold with vector field Electron. Res. Announc. Amer. Math. Soc. 2000 95 97

[3] Kolář, Ivan, Michor, Peter W., Slovák, Jan Natural operations in differential geometry 1993

[4] Kriegl, Andreas, Michor, Peter W. The convenient setting of global analysis 1997

[5] Palais, Richard S. A global formulation of the Lie theory of transformation groups Mem. Amer. Math. Soc. 1957

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