Stable rank for crossed products by actions of finite groups on C*-algebras

2017/08/08 by Hiroyuki Osaka, Osaka, Hiroyuki
Mathematics · Physics and Astronomy · #46L35 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1708.02665

openalex publication_date 2017/08/08 · openalex created_date 2017/08/17 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group, A a unital separable finite simple nuclear C*-algebra, and α an action of G on A. Assume that A absorbs the Jiang-Su algebra Z, the extremal boundary of the trace space of A is compact and finite dimensional and that α fixes any tracial state of A. Then tsr(A \rtimes_αG) = 1. In particular, when A has a unique tracial state, we conclude it without above conditons on a tracial state space of A.

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