Final group topologies, Kac-Moody groups and Pontryagin duality
By Helge Glöckner, Ralf Gramlich, Tobias Hartnick. 2006
54 citations recorded by the source corpus.
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 kω-space, or locally kω. 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 kω-groups). Our second application concerns Pontryagin duality theory for the classes of almost metrizable topological abelian groups, resp., locally kω 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 kω abelian groups.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/aace463a3e74bd89412175a6473f1206759c1c7a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Differentiable mappings on products with different degrees of differentiability in the two factors (2012, background): “Likewise, the product of two hemicompact k-spaces(2) (also known as kω-spaces) is a hemicompact k-space and hence a k-space (see [10] for further information and [22], including analogues for spaces which are only locally kω).”