Final group topologies, Kac-Moody groups and Pontryagin duality
Identifieur interne : 000428 ( Main/Exploration ); précédent : 000427; suivant : 000429Final group topologies, Kac-Moody groups and Pontryagin duality
Auteurs : Helge Glöckner [Allemagne] ; Ralf Gramlich [Allemagne, Royaume-Uni] ; Tobias Hartnick [Suisse]Source :
- Israel Journal of Mathematics [ 0021-2172 ] ; 2010-06-01.
Abstract
Abstract: We study final group topologies and their relations to compactness properties. In particular, we are interested in situations where a colimit or direct limit is locally compact, a k ω-space, or locally k ω. As a first application, we show that unitary forms of complex Kac-Moody groups can be described as the colimit of an amalgam of subgroups (in the category of Hausdorff topological groups, and the category of k ω-groups). Our second application concerns Pontryagin duality theory for the classes of almost metrizable topological abelian groups, resp., locally k ω topological abelian groups, which are dual to each other. In particular, we explore the relations between countable projective limits of almost metrizable abelian groups and countable direct limits of locally k ω abelian groups.
Url:
DOI: 10.1007/s11856-010-0038-5
Affiliations:
- Allemagne, Royaume-Uni, Suisse
- Angleterre, Canton de Zurich, District de Darmstadt, Hesse (Land), Midlands de l'Ouest
- Birmingham, Darmstadt, Zurich
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J. Math.</title><idno type="ISSN">0021-2172</idno><idno type="eISSN">1565-8511</idno><imprint><publisher>The Hebrew University Magnes Press</publisher><pubPlace>Heidelberg</pubPlace><date type="published" when="2010-06-01">2010-06-01</date><biblScope unit="volume">177</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="49">49</biblScope><biblScope unit="page" to="101">101</biblScope></imprint><idno type="ISSN">0021-2172</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0021-2172</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We study final group topologies and their relations to compactness properties. In particular, we are interested in situations where a colimit or direct limit is locally compact, a k ω-space, or locally k ω. 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