Freeness of actions of finite groups on C*-algebras

2009/02/27 by N. Christopher Phillips, Phillips, N. Christopher · 1 citation
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.0902.4891

40 pages; AMSLaTeX. Submitted to the proceedings of the workshop "Operator Structures and Dynamical Systems", Leiden, July 2008

arxiv created 2009/02/27 · openalex publication_date 2009/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe some of the forms of freeness of group actions on noncommutative C*-algebras that have been used, with emphasis on actions of finite groups. We give some indications of their strengths, weaknesses, applications, and relationships to each other. The properties discussed include the Rokhlin property, K-theoretic freeness, the tracial Rokhlin property, pointwise outerness, saturation, hereditary saturation, and the requirement that the strong Connes spectrum be the entire dual.

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• The relative radius of comparison of the crossed product of a non-unital C*-algebra by a finite group

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