ON LIE ALGEBRA ACTIONS

被引：0
|
作者：
Cushman, Richard H. [1 ]
Sniatycki, Jedrzej [1 ]
机构：
[1] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2020年 / 13卷 / 04期
关键词：
Lie algebra action; proper action; differential space; subcartesian; completely integrable;
D O I：
10.3934/dcdss.2020066
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：1115 / 1129
页数：15
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