Intermediate subalgebras for reduced crossed products of discrete groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911900856483840 |
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| author | Kennedy, Matthew Ursu, Dan |
| author_facet | Kennedy, Matthew Ursu, Dan |
| contents | 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 $A \subseteq A \rtimes_{α,λ} Γ$ and partial subactions of $α$. This condition, which we refer to as pointwise residual proper outerness, is a natural noncommutative generalization of freeness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01546 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intermediate subalgebras for reduced crossed products of discrete groups Kennedy, Matthew Ursu, Dan Operator Algebras Functional Analysis 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 $A \subseteq A \rtimes_{α,λ} Γ$ and partial subactions of $α$. This condition, which we refer to as pointwise residual proper outerness, is a natural noncommutative generalization of freeness. |
| title | Intermediate subalgebras for reduced crossed products of discrete groups |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2406.01546 |