The ideal structure of reduced crossed products

2008/04/23 by Adam Sierakowski, Sierakowski, Adam · 1 citation
Mathematics · #46L55 (Primary) #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.0804.3772

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

arxiv created 2009/03/16 · arxiv updated 2009/12/01

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.

Cited by

• A Banach *-algebra associated with the action of a group on a topological space

Related

• Primality and the ideal intersection property for reduced crossed products
• Uniformly recurrent subgroups and the ideal structure of reduced crossed products
• Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems
• Reduced twisted crossed products over C*-simple groups
• Inducing Primitive Ideals