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Uniform property
$ \Gamma $ and finite dimensional tracial boundaries
- Part of
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- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 05 March 2025, pp. 1-22
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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 $.
