Uniform property $Γ$ and finite dimensional tracial boundaries
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912133445320704 |
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| author | Evington, Samuel Schafhauser, Christopher |
| author_facet | Evington, Samuel Schafhauser, Christopher |
| contents | We prove that a C$^*$-algebra $A$ has uniform property $Γ$ if the set of extremal tracial states, $\partial_e T(A)$, is a non-empty compact space of finite covering dimension and for each $τ\in \partial_e T(A)$, the von Neumann algebra $π_τ(A)''$ arising from the GNS representation has property $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform property $Γ$ and finite dimensional tracial boundaries Evington, Samuel Schafhauser, Christopher Operator Algebras We prove that a C$^*$-algebra $A$ has uniform property $Γ$ if the set of extremal tracial states, $\partial_e T(A)$, is a non-empty compact space of finite covering dimension and for each $τ\in \partial_e T(A)$, the von Neumann algebra $π_τ(A)''$ arising from the GNS representation has property $Γ$. |
| title | Uniform property $Γ$ and finite dimensional tracial boundaries |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2407.16612 |