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Social and Behavioral Sciences Commons

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Crossed

2010

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Full-Text Articles in Social and Behavioral Sciences

The Ideal Structure Of Reduced Crossed Products, Adam Sierakowski Jan 2010

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 …