Full and reduced coactions of locally compact groups on C*-algebras

Astrid An Huef, John Quigg, Iain Raeburn, Dana P. Williams

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Abstract

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we use definitions and constructions that are well documented and accessible to non-experts, and otherwise we provide full details. We then give a series of applications to illustrate the use of these techniques. We obtain in particular a new version of Mansfield's imprimitivity theorem for full coactions, and prove that it gives a natural isomorphism between crossed-product functors defined on appropriate categories.

Original languageEnglish (US)
Pages (from-to)3-23
Number of pages21
JournalExpositiones Mathematicae
Volume29
Issue number1
DOIs
StatePublished - Jan 1 2011

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Keywords

  • Coaction
  • Crossed product
  • Fixed-point algebra
  • Landstad's duality
  • Proper action

ASJC Scopus subject areas

  • Mathematics(all)

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