Precompact groups and property (T)
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Scholar |
Otros documentos de la autoría: Ferrer González, María Vicenta; Hernández, Salvador; Uspenskij, Vladimir
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Mostrar el registro completo del ítemcomunitat-uji-handle:10234/9
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http://dx.doi.org/10.1016/j.jmaa.2013.03.004 |
Metadatos
Título
Precompact groups and property (T)Fecha de publicación
2013-08Editor
ElsevierCita bibliográfica
FERRER, M.; HERNÁNDEZ, S.; USPENSKIJ, V. Precompact groups and property (T). Journal of Mathematical Analysis and Applications, 2013, 404.2: 221-230.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://www.sciencedirect.com/science/article/pii/S0022247X13001960Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
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. [-]
Publicado en
Journal of Mathematical Analysis and Applications Volume 404, Issue 2, 15 August 2013Derechos de acceso
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