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The Ideal Structure Of Reduced Crossed Products, Adam Sierakowski

Faculty of Engineering and Information Sciences - Papers: Part A

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 A ⋊r G. When A separates the ideals in A ⋊r G, then there is a one-to-one correspondence between the ideals in A ⋊r G 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 …