Precompact groups and property (T)
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Other documents of the author: Ferrer González, María Vicenta; Hernández, Salvador; Uspenskij, Vladimir
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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http://dx.doi.org/10.1016/j.jmaa.2013.03.004 |
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Title
Precompact groups and property (T)Date
2013-08Publisher
ElsevierBibliographic citation
FERRER, M.; HERNÁNDEZ, S.; USPENSKIJ, V. Precompact groups and property (T). Journal of Mathematical Analysis and Applications, 2013, 404.2: 221-230.Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0022247X13001960Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
For a topological group GG, the dual object View the MathML sourceĜ is defined as the set of equivalence classes of irreducible unitary representations of GG equipped with the Fell topology. It is well known that, ... [+]
For a topological group GG, the dual object View the MathML sourceĜ is defined as the set of equivalence classes of irreducible unitary representations of GG equipped with the Fell topology. It is well known that, if GG is compact, View the MathML sourceĜ is discrete. In this paper, we investigate to what extent this remains true for precompact groups, that is, dense subgroups of compact groups. We show that: (a) if GG is a metrizable precompact group, then View the MathML sourceĜ is discrete; (b) if GG is a countable non-metrizable precompact group, then View the MathML sourceĜ is not discrete; (c) every non-metrizable compact group contains a dense subgroup GG for which View the MathML sourceĜ is not discrete. This extends to the non-Abelian case what was known for Abelian groups. We also prove that, if GG is a countable Abelian precompact group, then GG does not have Kazhdan’s property (T), although View the MathML sourceĜ is discrete if GG is metrizable. [-]
Is part of
Journal of Mathematical Analysis and Applications Volume 404, Issue 2, 15 August 2013Rights
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