Coaction functors, II

Steven Kaliszewski, Magnus B. Landstad, John Quigg

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

In their study of the application of crossed-product functors to the Baum- Connes conjecture, Buss, Echterhoff, and Willett introduced various properties that crossed-product functors may have. Here we introduce and study analogues of some of these properties for coaction functors, making sure that the properties are preserved when the coaction functors are composed with the full crossed product to make a crossed-product functor. The new properties for coaction functors studied here are functoriality for generalized homomorphisms and the correspondence property. We also study the connections with the ideal property. The study of functoriality for generalized homomorphisms requires a detailed development of the Fischer construction of maximalization of coactions with regard to possibly degenerate homomorphisms into multiplier algebras. We verify that all "KLQ" functors arising from large ideals of the Fourier-Stieltjes algebra B.G/ have all the properties we study, and at the opposite extreme we give an example of a coaction functor having none of the properties.

Original languageEnglish (US)
Pages (from-to)301-339
Number of pages39
JournalPacific Journal of Mathematics
Volume293
Issue number2
DOIs
Publication statusPublished - Jan 1 2018

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Keywords

  • Action
  • Coaction
  • Crossed product
  • Exact sequence
  • Fourier-Stieltjes algebra
  • Morita compatible

ASJC Scopus subject areas

  • Mathematics(all)

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