统一属性 $Γ$ 和有限维三维边界

arXiv - MATH - Operator Algebras Pub Date : 2024-07-23 DOI:arxiv-2407.16612

Samuel Evington, Christopher Schafhauser

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引用次数: 0

摘要

我们证明，如果极端三态的集合 $\partial_e T(A)$ 是一个无限覆盖维度的非空紧凑空间，并且对于 \partial_e T(A)$ 中的每个 $\tau ，由 GNS 表示产生的 vonNeumann 代数 $\pi_\tau(A)''$ 具有统一性质 $\Gamma $，那么 C$^*$-algebra $A$ 就具有统一性质 $/Gamma$。

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Uniform property $Γ$ and finite dimensional tracial boundaries

We prove that a C$^*$-algebra $A$ has uniform property $\Gamma$ if the set of extremal tracial states, $\partial_e T(A)$, is a non-empty compact space of finite covering dimension and for each $\tau \in \partial_e T(A)$, the von Neumann algebra $\pi_\tau(A)''$ arising from the GNS representation has property $\Gamma$.

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arXiv - MATH - Operator Algebras

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