The Structure of Differential Invariants for a Free Symmetry Group Action

被引：0
|
作者：
Magazev, A. A. [1 ]
Shirokov, I. V. [1 ]
机构：
[1] Omsk State Tech Univ, Omsk 644050, Russia
来源：
RUSSIAN MATHEMATICS | 2023年 / 67卷 / 06期
基金：
俄罗斯科学基金会;
关键词：
symmetry group; differential invariant; free action; MOVING COFRAMES;
D O I：
10.3103/S1066369X23060051
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the paper, we consider the problem of describing the general structure of differential invariants for transformation groups that act freely and regularly. We formulate two theorems describing the structures of differential invariants for intransitive and transitive free actions, respectively. In both cases it is shown that the differential invariants can be expressed in terms of the symbols of right-invariant vector fields. Finally, we discuss prospects for solving the problem considered for more general group actions.
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页码：26 / 33
页数：8
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