Completing Lie algebra actions to Lie group actions
Authors:
Franz W. Kamber and Peter W. Michor
Journal:
Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 1-10
MSC (2000):
Primary 22F05, 37C10, 54H15, 57R30, 57S05
DOI:
https://doi.org/10.1090/S1079-6762-04-00124-6
Published electronically:
February 18, 2004
MathSciNet review:
2048426
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Abstract | References | Similar Articles | Additional Information
Abstract: 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.
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Additional Information
Franz W. Kamber
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801
Email:
kamber@math.uiuc.edu
Peter W. Michor
Affiliation:
Institut für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria, and Erwin Schrödinger Institut für Mathematische Physik, Boltzmanngasse 9, A-1090 Wien, Austria
MR Author ID:
124340
Email:
michor@esi.ac.at
Keywords:
$\mathfrak {g}$-manifold,
$G$-manifold,
foliation
Received by editor(s):
October 27, 2003
Published electronically:
February 18, 2004
Additional Notes:
FWK and PWM were supported by ‘Fonds zur Förderung der wissenschaftlichen Forschung, Projekt P 14195 MAT’
Communicated by:
Alexandre Kirillov
Article copyright:
© Copyright 2004
American Mathematical Society