Extension of unitary representations of inductive limits of finite dimensional Lie groups
type: Item
instance of: scholarly article
title: Extension of unitary representations of inductive limits of finite dimensional Lie groups
zbMATH Open document ID: 0699.22019
DOI: 10.1016/0034-4877(88)90029-8
published in: Reports on Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: The author proves that every continuous unitary representation of the inductive limit \[ GL({\mathbb{Z}},{\mathbb{R}})=\lim_{\vec n}GL(2n+1,{\mathbb{R}}) \] of general linear groups can be extended by continuity to the unitary representation of a Hilbert-Lie group \(GL_ 2(a)\) (which depends on the starting representation) with \[ GL({\mathbb{Z}},{\mathbb{R}})=\lim_{\vec a}GL_ 2(a). \]
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 22E65
zbMATH DE Number: 4146295
zbMATH Keywords: continuous unitary representation
zbMATH Keywords: inductive limit
zbMATH Keywords: general linear groups
zbMATH Keywords: Hilbert-Lie group
Wikidata QID: Q115364227
author: A. V. Kosyak
reviewed by: Evelyn Weimar-Woods
MaRDI profile type: Publication
full work available at URL: 0034-4877(88)90029-8
OpenAlex ID: W2087659824
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description: scientific article; zbMATH DE number 4146295