Final group topologies, Kac-Moody groups and Pontryagin duality

Details Final group topologies, Kac-Moody groups and Pontryagin duality Final group topologies, Kac-Moody groups and Pontryagin duality

2006-03-22

arxiv.org/abs/math/0603537v3

Mathematics

Group Theory

v3: exposition improved; former title "Final group topologies, Phan systems and Pontryagin duality'' replaced by new title

Scientific paper

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_\omega-space, or locally k_\omega. 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_\omega-groups). Our second application concerns Pontryagin duality theory for the classes of almost metrizable topological abelian groups, resp., locally k_\omega 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_\omega abelian groups.

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