A Criterion for Z-Stability with Applications to Crossed Products

2015/07/27 by Julian Buck, Buck, Julian
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1507.07524

Abstract

Building on an argument by Toms and Winter, we show that if A is a simple, separable, unital, Z-stable C*-algebra, then the crossed product of C(X,A) by an automorphism is also Z-stable, provided that the automorphism induces a minimal homeomorphism on X. As a consequence, we observe that if A is nuclear and purely infinite then the crossed product is a Kirchberg algebra.

Related

• The structure of crossed products by automorphisms of C (X, D)
• Z-stability of crossed products by strongly outer actions
• Stable rank of C(X)\rtimesΓ
• Dynamical comparison and Z-stability for crossed products of simple C^*-algebras
• A homotopy rigidity theorem for Z₀-stable C^∗-algebras