Final group topologies,Kac-Moody groups and Pontryagin duality |
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Authors: | Helge Glöckner Ralf Gramlich Tobias Hartnick |
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Affiliation: | 1.Universit?t Paderborn, Institut für Mathematik,Paderborn,Germany;2.TU Darmstadt, FB Mathematik AGF,Darmstadt,Germany;3.The University of Birmingham School of Mathematics,Edgbaston,UK;4.Departement Mathematik,Zürich,Switzerland |
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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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