Proper actions, fixed-point algebras and naturality in nonabelian duality

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Suppose a locally compact group G acts freely and properly on a locally compact Hausdorff space X, and let γ be the induced action on C0 (X). We consider a category in which the objects are C*-dynamical systems (A, G, α) for which there is an equivariant homomorphism of (C0 (X), γ) into the multiplier algebra M (A). Rieffel has shown that such systems are proper and saturated, and hence have a generalized fixed-point algebra Aα which is Morita equivalent to A ×α, r G. We show that the assignment (A, α) {mapping} Aα is functorial, and that Rieffel's Morita equivalence is natural in a suitable sense. We then use our results to prove a categorical version of Landstad duality which characterizes crossed products by coactions, and to prove that Mansfield imprimitivity for crossed products by homogeneous spaces is natural.

Original languageEnglish (US)
Pages (from-to)2949-2968
Number of pages20
JournalJournal of Functional Analysis
Volume254
Issue number12
DOIs
StatePublished - Jun 15 2008

Fingerprint

Proper Action
Crossed Product
Duality
Fixed point
C*-dynamical System
Coaction
Multiplier Algebra
Morita Equivalence
Algebra
Compact Hausdorff Space
Locally Compact Group
Locally Compact
Homogeneous Space
Homomorphism
Equivariant
Categorical
Assignment
Object

Keywords

  • Coaction
  • Comma category
  • Crossed product
  • Fixed-point algebra
  • Landstad duality
  • Proper actions

ASJC Scopus subject areas

  • Analysis

Cite this

Proper actions, fixed-point algebras and naturality in nonabelian duality. / Kaliszewski, Steven; Quigg, John; Raeburn, Iain.

In: Journal of Functional Analysis, Vol. 254, No. 12, 15.06.2008, p. 2949-2968.

Research output: Contribution to journalArticle

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