Intermediate crossed product C^*-algebras

2023/11/02 by Amrutam, Tattwamasi, Hirshberg, Ilan, Seth, Apurva
#46L05 #46L10 #46L55 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2311.01524

Abstract

Let B be a separable C^*-algebra, let Γ be a discrete countable group, let α: Γ→ 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⊆ C ⊆ B \rtimes_α,r Γ is a crossed product of an intermediate invariant subalgebra A ⊆ C₀ ⊆ B by Γ. Those are used to generalize related results by Suzuki.

Related

• Intermediate subalgebras for reduced crossed products of discrete groups
• Perturbations of crossed product C*-algebras by amenable groups
• Purely infinite C*-algebras arising from crossed products
• Crossed product splitting of intermediate operator algebras via 2-cocycles
• C*-crossed products by partial actions and actions of inverse semigroups