Weakly tracially approximately representable actions

2021/10/13 by M. Ali Asadi-Vasfi, Asadi-Vasfi, M. Ali · 2 citations
Mathematics · Physics and Astronomy · #19K14 #46L55 #46L80 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2110.07081

openalex publication_date 2021/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a weak tracial analog of approximate representability under the name "weak tracial approximate representability" for finite group actions. Let G be a finite abelian group, let A be an infinite-dimensional simple unital C*-algebra, and let α\colon G → Aut (A) be an action of G on A which is pointwise outer. Then α has the weak tracial Rokhlin property if and only if the dual action \widehatα of the Pontryagin dual \widehatG on the crossed product C^*(G, A, α) is weakly tracially approximately representable, and α is weakly tracially approximately representable if and only if the dual action \widehatα has the weak tracial Rokhlin property. This generalizes the results of Izumi in 2004 and Phillips in 2011 on the dual actions of finite abelian groups on unital simple C*-algebras.

Cited by

• Crossed products by compact group actions with the weak tracial Rokhlin property
• The relative radius of comparison of the crossed product of a non-unital C*-algebra by a finite group

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