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arXiv · 2407.16612

Uniform property $\Gamma$ and finite dimensional tracial boundaries

Samuel Evington·Christopher Schafhauser
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Abstract

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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Samuel Evington, Christopher Schafhauser. 2024-07-23. Uniform property $\Gamma$ and finite dimensional tracial boundaries. https://arxiv.org/abs/2407.16612

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