Naturality of symmetric imprimitivity theorems

Astrid An Huef, Steven Kaliszewski, Iain Raeburn, Dana P. Williams

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

The first imprimitivity theorems identified the representations of groups or dynamical systems which are induced from representations of a sub-group. Symmetric imprimitivity theorems identify pairs of crossed products by different groups which are Morita equivalent and hence have the same representation theory. Here we consider commuting actions of groups H and K on a C*-algebra which are saturated and proper as defined by Rieffel in 1990. Our main result says that the resulting Morita equivalence of crossed products is natural in the sense that it is compatible with homomorphisms and induction processes.

Original languageEnglish (US)
Pages (from-to)2319-2327
Number of pages9
JournalProceedings of the American Mathematical Society
Volume141
Issue number7
DOIs
StatePublished - Apr 24 2013

Keywords

  • Crossed products
  • Fixed-point algebras
  • Naturality
  • Proper actions on C*-algebras
  • Symmetric imprimitivity theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Naturality of symmetric imprimitivity theorems'. Together they form a unique fingerprint.

  • Cite this