Tracial approximation and \cal Z-stability

2022/05/09 by Huaxin Lin, Lin, Huaxin
Mathematics · #46L35 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2205.04013

openalex publication_date 2022/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a unital separable non-elementary amenable simple stably finite C*-algebra such that its tracial state space has a σ-compact countable-dimensional extremal boundary. We show that A is \cal Z-stable if and only if it has strict comparison and stable rank one. We show that this result also holds for non-unital cases (which may not be Morita equivalent to unital ones).

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