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arXiv · 2311.01524

Intermediate crossed product $C^*$-algebras

Tattwamasi Amrutam·Ilan Hirshberg·Apurva Seth
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Abstract

Let $B$ be a separable $C^*$-algebra, let $Γ$ be a discrete countable group, let $α: Γ\to \text{Aut}(B)$ be an action, and let $A$ be an invariant subalgebra. We find certain freeness conditions which guarantee that any intermediate $C^*$-algebra $A \rtimes_{α,r} Γ\subseteq C \subseteq B \rtimes_{α,r} Γ$ is a crossed product of an intermediate invariant subalgebra $A \subseteq C_0 \subseteq B$ by $Γ$. Those are used to generalize related results by Suzuki.

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Tattwamasi Amrutam, Ilan Hirshberg, Apurva Seth. 2023-11-02. Intermediate crossed product $C^*$-algebras. https://arxiv.org/abs/2311.01524

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