Rokhlin Dimension and Inductive Limit Actions on AF-algebras

2024/05/27 by M Sureshkumar, M, Sureshkumar, Prahlad Vaidyanathan +1
Computer Science · Mathematics · #46L40 #46L55 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2405.17380

openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a separable, AF-algebra A and an inductive limit action on A of a finitely generated abelian group with finite Rokhlin dimension with commuting towers, we give a local description of the associated crossed product C*-algebra. In particular, when A is unital and α∈ Aut(A) is approximately inner and has the Rokhlin property, we conclude that A \rtimes_α ℤ is an A\mathbbT-algebra.

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