This article is cited in 1 paper

Construction of first-order invariant differential operators

O. L. Kurnyavko^a, I. V. Shirokov<sup>b

a</sup> Omsk Institute of Water Transport – branch of the Siberian State University of Water Transport, 4 Ivana Alekseeva str., Omsk, 644043 Russia
^b Omsk State Technical University, 11 Mira Ave., Omsk, 644050 Russia

Abstract: The paper considers the problem of constructing systems of vector fields that are invariant under the action of the local Lie group of transformations. It is shown that there exists a special class of Lie groups for which this problem can be solved elementarily.

Keywords: Lie algebra, Lie group, invariant differential operator, left-invariant vector field, right-invariant vector field, invariant differentiation operator.

UDC: 512.81

Received: 13.03.2023
Revised: 17.08.2023
Accepted: 26.09.2023

DOI: 10.26907/0021-3446-2024-5-37-46

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2024, 68:5, 27–34