Continuity conditions for finite-dimensional representations of some locally bounded groups
type: Item
instance of: scholarly article
title: Continuity conditions for finite-dimensional representations of some locally bounded groups
zbMATH Open document ID: 1117.22003
DOI: 10.1134/S1061920806040078
published in: Russian Journal of Mathematical Physics
publication date: 2007-03-26T00:00:00Z
review text: The author proves necessary and sufficient conditions for the continuity of finite-dimensional representations of some topological groups. The conditions are formulated in terms of the variation of the representation at the identity of the group. The conditions are found for the following groups: -- locally oddly divisible groups; -- topological groups in which the open normal subgroups form a neighborhood base of the identity; -- almost divisible, non-discrete, locally pseudo-compact groups; -- (almost) connected locally compact groups. An application of the above result to the approximation of continuous quasirepresentations of almost connected locally compact groups is given.
reviewed by: Leszek Skrzypczak
Mathematics Subject Classification ID: 22D12
Mathematics Subject Classification ID: 22D05
zbMATH DE Number: 5136642
zbMATH Keywords: finite-dimensional representations
zbMATH Keywords: topological groups
author: A. I. Shtern
MaRDI profile type: Publication
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full work available at URL: s1061920806040078
OpenAlex ID: W2060440227
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description: scientific article; zbMATH DE number 5136642