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.

引用

页码：1115 / 1129

页数：15

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