Z-stability of crossed products by strongly outer actions

2009/12/24 by Hiroki Matui, Matui, Hiroki, Yasuhiko Sato +1
Mathematics · #46L40 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0912.4804

openalex publication_date 2009/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a certain class of unital simple stably finite C^*-algebras which absorb the Jiang-Su algebra Z tensorially. Under a mild assumption, we show that the crossed product of a C^*-algebra in this class by a strongly outer action of Z^N or a finite group is Z-stable. As an application, we also prove that all strongly outer actions of Z² on Z are mutually cocycle conjugate.

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