Crossed products by α-simple automorphisms on C*-algebras C(X,A)

2009/10/17 by Jiajie Hua, Hua, Jiajie
Mathematics · #46L35 #46L40 #46L55 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L35 #msc:46L40 #msc:46L55

paper · pdf · doi:10.48550/arxiv.0910.3299

14 pages

arxiv created 2010/06/07 · arxiv updated 2010/06/08

Abstract

Let X be a Cantor set, and let A be a unital separable simple amenable C*-algebra with tracial rank zero which satisfies the Universal Coefficient Theorem, we use C(X,A) to denote the set of all continuous functions from X to A, let α be an automorphism on C(X,A). Suppose that C(X,A) is α-simple and [α]=[id_{1⊗ A}] in KL(1⊗ A,1⊗ A), we show that C(X,A)\rtimes_αℤ has tracial rank zero.

Related

• The Rokhlin Property for Automorphisms on Simple C*-Algebras
• The Rohlin property for automorphisms on simple C*-algebras
• Stable and real rank for crossed products by automorphisms with the tracial Rokhlin property
• Tracial Rokhlin property for automorphisms on simple A\mathbb T-algebras
• Crossed Products by Automorphisms with the Tracial Quasi-Rokhlin Property