2019•Discrete and Continuous Dynamical Systems - SRequires access
On Lie algebra actions
Richard Cushman, Jędrzej Śniatycki
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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.