Stabilising uniform property Γ

Castillejos, Jorge; Evington, Samuel

doi:10.1090/proc/15553

Stabilising uniform property $\Gamma$
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by Jorge Castillejos and Samuel Evington

Proc. Amer. Math. Soc. 149 (2021), 4725-4737

DOI: https://doi.org/10.1090/proc/15553

Published electronically: August 4, 2021

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Abstract:

We introduce stabilised property $\Gamma$, a $\mathrm {C}^*$-algebraic variant of property $\Gamma$ which is invariant under stable isomorphism. We then show that simple separable nuclear $\mathrm {C}^*$-algebras with stabilised property $\Gamma$ and $\mathrm {Cu}(A) \cong \mathrm {Cu}(A \otimes \mathcal {Z})$ absorb the Jiang-Su algebra $\mathcal {Z}$ tensorially.

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