On Lie algebra actions

Richard H. Cushman; Jędrzej Śniatycki

doi:10.3934/dcdss.2020066

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2020, Volume 13, Issue 4: 1115-1129. Doi: 10.3934/dcdss.2020066

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On Lie algebra actions

Richard H. Cushman^, and
Jędrzej Śniatycki

Department of Mathematics and Statistics, University of Calgary, Calgary, AB, T2N 1N4, Canada

^* Corresponding author: R. H. Cushman
^* Corresponding author: R. H. Cushman

Received: September 30, 2017

Revised: June 30, 2018

Published: April 2020

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Abstract

In this paper we define an action of a Lie algebra on a smooth manifold. We get nearly the same results as those for group actions, when the flows of the symmetry vector fields are complete. We show that the orbit space of a Lie algebra action is a differential space. We discuss differential spaces occuring in the reduction of symmetries in integrable Hamiltonian systems.

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Mathematics Subject Classification: Primary: 37J15, 37J45; Secondary: 22F05.

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References

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