Precompact groups and property (T)
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http://dx.doi.org/10.1016/j.jmaa.2013.03.004 |
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Títol
Precompact groups and property (T)Data de publicació
2013-08Editor
ElsevierCita bibliogràfica
FERRER, M.; HERNÁNDEZ, S.; USPENSKIJ, V. Precompact groups and property (T). Journal of Mathematical Analysis and Applications, 2013, 404.2: 221-230.Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://www.sciencedirect.com/science/article/pii/S0022247X13001960Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
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. [-]
Publicat a
Journal of Mathematical Analysis and Applications Volume 404, Issue 2, 15 August 2013Drets d'accés
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