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Precompact groups and property (T)
dc.contributor.author | Ferrer González, María Vicenta | |
dc.contributor.author | Hernández, Salvador | |
dc.contributor.author | Uspenskij, Vladimir | |
dc.date.accessioned | 2014-05-16T06:49:08Z | |
dc.date.available | 2014-05-16T06:49:08Z | |
dc.date.issued | 2013-08 | |
dc.identifier.citation | FERRER, M.; HERNÁNDEZ, S.; USPENSKIJ, V. Precompact groups and property (T). Journal of Mathematical Analysis and Applications, 2013, 404.2: 221-230. | ca_CA |
dc.identifier.uri | http://hdl.handle.net/10234/92250 | |
dc.description.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, 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. | ca_CA |
dc.format.extent | 9 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Elsevier | ca_CA |
dc.relation.isPartOf | Journal of Mathematical Analysis and Applications Volume 404, Issue 2, 15 August 2013 | ca_CA |
dc.rights | (c) Elsevier | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
dc.subject | Compact group | ca_CA |
dc.subject | Precompact group | ca_CA |
dc.subject | Representation | ca_CA |
dc.subject | Pontryagin–van Kampen duality | ca_CA |
dc.subject | Compact-open topology | ca_CA |
dc.subject | Fell dual space | ca_CA |
dc.subject | Fell topology | ca_CA |
dc.subject | Bohr compactification | ca_CA |
dc.subject | Kazhdan property (T) | ca_CA |
dc.subject | Determined group | ca_CA |
dc.title | Precompact groups and property (T) | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | http://dx.doi.org/10.1016/j.jmaa.2013.03.004 | |
dc.rights.accessRights | info:eu-repo/semantics/restrictedAccess | ca_CA |
dc.relation.publisherVersion | http://www.sciencedirect.com/science/article/pii/S0022247X13001960 | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion |
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