The ideal structure of reduced crossed products

Details The ideal structure of reduced crossed products The ideal structure of reduced crossed products

2008-04-23

arxiv.org/abs/0804.3772v2

Mathematics

Operator Algebras

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

Scientific paper

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.

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