Intermediate subalgebras for reduced crossed products of discrete groups

2024/06/03 by Matthew Kennedy, Kennedy, Matthew, Dan Ursu +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2406.01546

openalex publication_date 2024/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let α: Γ\curvearrowright A be an action of a discrete group Γ on a unital C*-algebra A by *-automorphisms and let A \rtimes_α,λ Γ denote the corresponding reduced crossed product C*-algebra. Assuming that Γ satisfies the approximation property, we establish a sufficient and (almost always) necessary condition on the action α for the existence of a Galois correspondence between intermediate C*-algebras for the inclusion A ⊆ A \rtimes_α,λ Γ and partial subactions of α. This condition, which we refer to as pointwise residual proper outerness, is a natural noncommutative generalization of freeness.

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• Maximality and symmetry related to the \(2\)-adic ring \(C^*\)-algebra

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