The ideal structure of reduced crossed products

Abstract

Let (A,G) be a C*-dynamical system with G discrete. In this paper we investigate the ideal structure of the reduced crossed product C*-algebra and in particular we determine sufficient - and in some cases also necessary - conditions for A to separate the ideals in Ax_rG. When A separates the ideals in Ax_rG, then there is a one-to-one correspondence between the ideals in Ax_rG and the invariant ideals in A. We extend the concept of topological freeness and present a generalization of the Rokhlin property. Exactness properties of (A,G) turns out to be crucial in these investigations.

23 pages, relation to properly outer actions added, accepted in Muenster J. Math

References in corpus (2)

• On the Banach $\ast$-algebra crossed product associated with a topological dynamical system
• Embedding Crossed Products into a Unital Simple AF-algebra

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• The Furstenberg Boundary of a Groupoid
• On simplicity of intermediate C*-algebras
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