2017/05/18 by Christopher Schafhauser, Schafhauser, Christopher
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1705.06555
13 pages
arxiv created 2017/05/18 · openalex publication_date 2017/05/18 · arxiv updated 2017/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A trace τ on a separable C*-algebra A is called matricial field (MF) if there is a trace-preserving morphism from A to Qω, where Qω denotes the norm ultrapower of the universal UHF-algebra Q. In general, the trace τ induces a state on the Cuntz semigroup Cu(A). We show there is always a state-preserving morphism from Cu(A) to Cu(Qω). As an application, if A is an AI-algebra and F is a free group acting on A, then every trace on the reduced crossed product A \rtimes F is MF. This further implies the same result when A is an AH-algebra with the ideal property such that K1(A) is a torsion group. We also use this to characterize when A \rtimes F is MF (i.e. admits an isometric morphism into Qω) for many simple, nuclear C*-algebras A.