The ideal structure of reduced crossed products
Operator Algebras
2009-03-16 v2
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.
Cite
@article{arxiv.0804.3772,
title = {The ideal structure of reduced crossed products},
author = {Adam Sierakowski},
journal= {arXiv preprint arXiv:0804.3772},
year = {2009}
}
Comments
23 pages, relation to properly outer actions added, accepted in Muenster J. Math