Geodesic
Completing Lie algebra actions to Lie group actions
Kamber, Franz1 ; Michor, Peter2
1Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801
2Institut 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

Voir la notice de l'article

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 
@article{10_1090_S1079_6762_04_00124_6,
     author = {Kamber, Franz and Michor, Peter},
     title = {Completing {Lie} algebra actions to {Lie} group actions},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {1--10},
     year = {2004},
     volume = {10},
     doi = {10.1090/S1079-6762-04-00124-6},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-04-00124-6/}
}
TY  - JOUR
AU  - Kamber, Franz
AU  - Michor, Peter
TI  - Completing Lie algebra actions to Lie group actions
JO  - Electronic research announcements of the American Mathematical Society
PY  - 2004
SP  - 1
EP  - 10
VL  - 10
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-04-00124-6/
DO  - 10.1090/S1079-6762-04-00124-6
ID  - 10_1090_S1079_6762_04_00124_6
ER  - 
%0 Journal Article
%A Kamber, Franz
%A Michor, Peter
%T Completing Lie algebra actions to Lie group actions
%J Electronic research announcements of the American Mathematical Society
%D 2004
%P 1-10
%V 10
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-04-00124-6/
%R 10.1090/S1079-6762-04-00124-6
%F 10_1090_S1079_6762_04_00124_6
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

[1] Alekseevsky, D. V., Michor, Peter W. Differential geometry of 𝔤-manifolds Differential Geom. Appl. 1995 371 403

[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

Cité par Sources :