Noncommutative topological boundaries and amenable invariant random intermediate subalgebras
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913961402695680 |
|---|---|
| author | Zhou, Shuoxing |
| author_facet | Zhou, Shuoxing |
| contents | As an analogue of the topological boundary of discrete groups $Γ$, we define the noncommutative topological boundary of tracial von Neumann algebras $(M, τ)$ and apply it to generalize the main results of [AHO23], showing that for a trace-preserving action $Γ\curvearrowright (A, τ_A)$ on an amenable tracial von Neumann algebra, any $Γ$-invariant amenable intermediate subalgebra between $A$ and $Γ\ltimes A$ is necessarily a subalgebra of $\mathrm{Rad}(Γ) \ltimes A$. By taking $(A, τ_A) = L^\infty(X, ν_X)$ for a free pmp action $Γ\curvearrowright (X, ν_X)$, we obtain a similar result for the invariant subequivalence relations of $\mathcal{R}_{Γ\curvearrowright X}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noncommutative topological boundaries and amenable invariant random intermediate subalgebras Zhou, Shuoxing Operator Algebras Dynamical Systems Group Theory As an analogue of the topological boundary of discrete groups $Γ$, we define the noncommutative topological boundary of tracial von Neumann algebras $(M, τ)$ and apply it to generalize the main results of [AHO23], showing that for a trace-preserving action $Γ\curvearrowright (A, τ_A)$ on an amenable tracial von Neumann algebra, any $Γ$-invariant amenable intermediate subalgebra between $A$ and $Γ\ltimes A$ is necessarily a subalgebra of $\mathrm{Rad}(Γ) \ltimes A$. By taking $(A, τ_A) = L^\infty(X, ν_X)$ for a free pmp action $Γ\curvearrowright (X, ν_X)$, we obtain a similar result for the invariant subequivalence relations of $\mathcal{R}_{Γ\curvearrowright X}$. |
| title | Noncommutative topological boundaries and amenable invariant random intermediate subalgebras |
| topic | Operator Algebras Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2407.10905 |