Continuous subgroups of a generalized Euclidean group
type: Item
instance of: scholarly article
title: Continuous subgroups of a generalized Euclidean group
zbMATH Open document ID: 0603.22005
DOI: 10.1007/BF01056758
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The general method of classification with respect to certain conjugacy of subalgebras of a finite dimensional Lie algebra L with nontrivial abelian ideal N and semisimple quotient algebra L/N is well known. The problem of classification of subalgebras of the Euclidean algebra LE(n) with respect to E(n)-conjugacy is reduced in the paper under review to the description of the irreducible parts of subalgebras of the algebra LO(n) with respect to O(n)-conjugacy. As an application of the general results, the description of the maximal abelian subalgebras of LE(n), \(n\geq 2\), and all subalgebras of LE(5) is given.
Mathematics Subject Classification ID: 22E60
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 20H20
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 3973189
zbMATH Keywords: groups of transformations
zbMATH Keywords: subgroups of Euclidean group
zbMATH Keywords: conjugacy of subalgebras
zbMATH Keywords: Euclidean algebra
author: W. I. Fushchich
author: Anatoliy Barannyk
author: Leonid F. Barannyk
reviewed by: A. Fleischer
MaRDI profile type: Publication
cites work: Continuous subgroups of the fundamental groups of physics. I. General method and the Poincaré group
cites work: Q3208916
cites work: Q3944795
cites work: Subgroups of the Euclidean group and symmetry breaking in nonrelativistic quantum mechanics
full work available at URL: https://doi.org/10.1007/bf01056758
OpenAlex ID: W2055092951
description: scientific article; zbMATH DE number 3973189