On covariant realizations of the Euclid group
type: Item
instance of: scholarly article
title: On covariant realizations of the Euclid group
zbMATH Open document ID: 0957.22023
author: V. I. Lagno
author: R. Z. Zhdanov
author: W. I. Fushchich
published in: Communications in Mathematical Physics
publication date: 2001-03-22T00:00:00Z
review text: The authors classify realizations of the Lie algebras of the rotation group \(O(3)\) and the Euclidean group E(3) within the class of first order differential operators in arbitrary finite dimensions. It is found that there are only two different realizations of the Lie algebra of the group \(O(3)\) which are inequivalent within the action of the group of diffeomorphisms. A subclass of covariant realizations is described. Realizations of the Lie algebras corresponding to the groups \(O(4)\) and \(E(4)\) are also considered.
Mathematics Subject Classification ID: 22E60
Mathematics Subject Classification ID: 17B66
zbMATH DE Number: 1523443
zbMATH Keywords: rotation group
zbMATH Keywords: Euclid group
zbMATH Keywords: covariant realization
zbMATH Keywords: first order differential operators
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
full work available at URL: s002200000222
OpenAlex ID: W2131825920
DOI: 10.1007/S002200000222
Recommended article: On covariant realizations of the Poincaré group \(P(1,3)\)
Recommended article: Q3842223
Recommended article: Q4261428
Recommended article: Q4854005
Recommended article: The euclidean bianchi group
Recommended article: On covariants in exterior algebras for the even special orthogonal group
Recommended article: Realizing finite groups in Euclidean space
Recommended article: THE COVARIANT PICARD GROUPOID IN DIFFERENTIAL GEOMETRY
Recommended article: Covariant functional calculi from the affine groups
Recommended article: Q3487665
description: scientific article; zbMATH DE number 1523443