Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

Topologically free actions and ideals in discrete C*-dynamical systems

R. J. Archbolda1 and J. S. Spielberga2*

a1 Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB9 2TY, Scotland

a2 Department of Mathematics, Arizona State University, Tempe, AZ85287, USA

Abstract

A C*-dynamical system is called topologically free if the action satisfies a certain natural condition weaker than freeness. It is shown that if a discrete system is topologically free then the ideal structure of the crossed product algebra is related to that of the original algebra. One consequence is that a minimal topologically free discrete system has a simple reduced crossed product. Sharper results are obtained when the algebra is abelian.

(Received June 27 1992)

Footnotes

* Supported in part by SERC (UK) grant GR/F 74738, and by NSF (USA) grant DMS-9102971.