Centrally pure C*-algebras

2025/12/19 by Perera, Francesc, Thiel, Hannes, Vilalta, Eduard
#46L80 #46L85 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L05 #Secondary 19K14

paper · doi:10.48550/arxiv.2512.17261

Abstract

We show that a separable C*-algebra A is Z-stable if and only if its uncorrected central sequence algebra A' ∩ A_U is pure, if and only if Kirchberg's central sequence algebra F(A) is pure. More generally, we show that a C*-algebra A is separably Z-stable if and only if the relative central sequence algebra B' ∩ A_U is pure for every separable subalgebra B ⊆ A_U.

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Related

• A dichotomy for central sequence algebras
• Commutativity of central sequence algebras
• A non-stable C*-algebra with an elementary essential composition series
• A homotopy rigidity theorem for Z₀-stable C^∗-algebras
• Regularity properties in the classification program for separable amenable C*-algebras