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Final group topologies, Kac-Moody groups and Pontryagin duality

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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.

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Authors and Affiliations

  1. Universität Paderborn, Institut für Mathematik, Warburger Str. 100, 33098, Paderborn, Germany

    Helge Glöckner

  2. TU Darmstadt, FB Mathematik AGF, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    Ralf Gramlich

  3. The University of Birmingham School of Mathematics, Edgbaston, Birmingham, B15 2TT, UK

    Ralf Gramlich

  4. Departement Mathematik, Rämistrasse 101, 8092, Zürich, Switzerland

    Tobias Hartnick

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  1. Helge Glöckner
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  2. Ralf Gramlich
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Correspondence to Helge Glöckner.

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Glöckner, H., Gramlich, R. & Hartnick, T. Final group topologies, Kac-Moody groups and Pontryagin duality. Isr. J. Math. 177, 49–101 (2010). https://doi.org/10.1007/s11856-010-0038-5

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