Proper actions which are not saturated

Title: Proper actions which are not saturated
Creator: Marelli, Damián; Raeburn, Iain
Relation: Proceedings of the American Mathematical Society Vol. 137, Issue 7, p. 2273-2283
Publisher Link: http://dx.doi.org/10.1090/S0002-9939-09-09867-0
Publisher: American Mathematical Society
Resource Type: journal article
Date: 2009
Description: If a locally compact group G acts properly on a locally compact space X, then the induced action on C₀(X) is proper in the sense of Rieffel, with generalised fixed-point algebra C₀(GX). Rieffel's theory then gives a Morita equivalence between C₀(GX) and an ideal I in the crossed product C₀(X) x G; we identify I by describing the primitive ideals which contain it, and we deduce that I = C₀(X) x G if and only if G acts freely. We show that if a discrete group G acts on a directed graph E and every vertex of E has a finite stabiliser, then the induced action ∝ of G on the graph C* -algebra C*(E) is proper. When G acts freely on E, the generalised fixed-point algebra C*(E)∝ is isomorphic to C*(GE) and Morita equivalent to C*(E) x G, in parallel with the situation for free and proper actions on spaces, but this parallel does not seem to give useful predictions for nonfree actions.
Subject: Morita; algebra; Rieffel
Identifier: http://hdl.handle.net/1959.13/917012
Identifier: uon:8181
Identifier: ISSN:0002-9939
Language: eng
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