Strength of convergence in non-free transformation groups

Robert J Archbold, Astrid an Huef

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1 Citation (Scopus)

Abstract

Let (G,X) be a transformationgroup where the groupG does not necessarily act freely on the space X. We investigate the extent to which the action of G may fail to be proper. Stability subgroups are used to define new notions of strength of convergence in the orbit space and of measure accumulation along orbits. By using the representation theory of the associated crossed product C¿-algebra, we show that these notions are equivalent under certain conditions.
Original languageEnglish
Pages (from-to)819-845
Number of pages27
JournalJournal of Functional Analysis
Volume263
Issue number4
Early online date18 May 2012
DOIs
Publication statusPublished - 15 Aug 2012

Keywords

  • transformation group
  • stability subgroup
  • orbit space
  • proper action
  • k-Times convergence
  • measure accumulation
  • crossed-product C¿-algebra
  • induced representation
  • spectrum of a C¿-algebra
  • multiplicity of a representation

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