Extensions of pure C*-algebras

Fuente: arXiv
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Main Authors: Perera, Francesc, Thiel, Hannes, Vilalta, Eduard
Format: Preprint
Published: 2025
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author Perera, Francesc
Thiel, Hannes
Vilalta, Eduard
author_facet Perera, Francesc
Thiel, Hannes
Vilalta, Eduard
contents Given a closed ideal $I$ in a C*-algebra $A$, we show that $A$ is pure if and only if $I$ and $A/I$ are pure. More generally, we study permanence of comparison and divisibility properties when passing to extensions. As an application we show that stable multiplier algebras of reduced free group C*-algebras are pure.
format Preprint
id arxiv_https___arxiv_org_abs_2506_10529
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Extensions of pure C*-algebras
Perera, Francesc
Thiel, Hannes
Vilalta, Eduard
Operator Algebras
Primary 46L05, Secondary 19K14, 46L80, 46L85
Given a closed ideal $I$ in a C*-algebra $A$, we show that $A$ is pure if and only if $I$ and $A/I$ are pure. More generally, we study permanence of comparison and divisibility properties when passing to extensions. As an application we show that stable multiplier algebras of reduced free group C*-algebras are pure.
title Extensions of pure C*-algebras
topic Operator Algebras
Primary 46L05, Secondary 19K14, 46L80, 46L85
url https://arxiv.org/abs/2506.10529