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arXiv · 2506.10529

Extensions of pure C*-algebras

Francesc Perera·Hannes Thiel·Eduard Vilalta
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Abstract

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.

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Francesc Perera, Hannes Thiel, Eduard Vilalta. 2025-06-12. Extensions of pure C*-algebras. https://arxiv.org/abs/2506.10529

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