Purely infinite C*-algebras arising from crossed products
By M. Rørdam, Adam Sierakowski. Ergodic Theory and Dynamical Systems, 2010
83 citations recorded by the source corpus.
Abstract We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a commutative C*-algebra, where our sufficient conditions can be phrased in terms of paradoxicality of subsets of the spectrum of the abelian C*-algebra. As an application of our results we show that every discrete countable non-amenable exact group admits a free amenable minimal action on the Cantor set such that the corresponding crossed product C*-algebra is a Kirchberg algebra in the UCT class.
Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/6fa89c0f2d64938d3dbce39a3c321dd6723db4d8
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In Algebra and Number Theory
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In Statistical and Nonlinear Physics
Citations in the corpus
- Topological full groups of one-sided shifts of finite type (2012, unknown): “Sierakowski [39] (see Definition 4.”
- Dimension, comparison, and almost finiteness (2017, background): “1 of [37], every state σ on S(X,G) gives rise to a measure μ in MG(X) satisfying μ(A) = σ([1A]) for every clopen set A ⊆ X .”
- Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions☆ (2012, background): “As a biproduct of our results, we are able to answer a question raised in recent papers by Kerr [36], Kerr and Nowak [37], and Rørdam and Sierakowski [52].”