Stability of the van der Waerden theorem on the continuity of homomorphisms of compact semisimple Lie groups
type: Item
instance of: scholarly article
title: Stability of the van der Waerden theorem on the continuity of homomorphisms of compact semisimple Lie groups
zbMATH Open document ID: 1122.22001
published in: Applied Mathematics and Computation
publication date: 2007-06-13T00:00:00Z
review text: Let \(G\) be a compact semisimple Lie group and let \(U(N)\) be the group of unitary \(N\times N\) matrices. It is proved that if \(\rho:G\to U(N)\) is a map, for which \[ \| \rho(fg)-\rho(f)\rho(g)\| ,\quad f,\,g\in G, \] is uniformly small enough, then \(\rho\) is a small perturbation of an ordinary unitary representation of \(G\) into \(U(N)\).
reviewed by: Vladimir V. Peller
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 5163953
zbMATH Keywords: topological group
zbMATH Keywords: Lie group
zbMATH Keywords: group representation
zbMATH Keywords: amenable Banach algebra
Wikidata QID: Q115361855
author: A. I. Shtern
MaRDI profile type: Publication
full work available at URL: j.amc.2006.08.145
OpenAlex ID: W1963981164
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DOI: 10.1016/J.AMC.2006.08.145
description: scientific article; zbMATH DE number 5163953