The Automorphism group of a simple Z-stable C^*-algebra

2010/03/11 by Ping Wong Ng, Ng, Ping Wong, Efren Ruiz +1
Mathematics · #46L35 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L35

paper · pdf · doi:10.48550/arxiv.1003.2404

Improved the exposition of Section 3 and Section 4, added other references

arxiv created 2011/11/05 · arxiv updated 2011/11/08

Abstract

We study the automorphism group of a unital, simple, Z-stable C^*-algebra. In this paper, we generalize the results by the authors in \citepr_auto to Z-stable C^*-algebras \mathfrakA such that \mathfrakA ⊗ \mathfrakB is a separable, nuclear, simple, tracially AI algebras satisfying the Universal Coefficient Theorem (UCT) of Rosenberg and Schochet \citeuct. By the results of Lin in \citehl_asyunit and Winter in \citeww_localelliott, C^∗-algebras that satisfies the above condition are classified via K-theory and traces.

Related

• Classification of homomorphisms into simple Z-stable C^*-algebras
• Equivariant Z-stability for single automorphisms on simple C^*-algebras with tractable trace simplices
• A classification of finite simple amenable \cal Z-stable C^*-algebras, I: C^*-algebras with generalized tracial rank one
• Classification of finite simple amenable \cal Z-stable C^*-algebras
• Structure of the group of automorphisms of C^*-algebras