Stabilising uniform property $\Gamma $

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 04 Aug 2021Embargo end date: 01 Jan 2020 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 149, pages 4,725-4,737 (issn: 0002-9939, eissn: 1088-6826,

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Authors: Jorge Castillejos; Samuel Evington;

doi: 10.1090/proc/15553 , 10.48550/arxiv.2010.05792

arXiv: 2010.05792

Stabilising uniform property $\Gamma $

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Abstract

We introduce stabilised property Gamma, a C*-algebraic variant of property Gamma which is invariant under stable isomorphism. We then show that simple separable nuclear 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.

Proc. Amer. Math. Soc., to appear. Minor changes. Accepted version

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Keywords

Jiang-Su stability, Classifications of $C^*$-algebras, property Gamma, Mathematics - Operator Algebras, FOS: Mathematics, 46L05, 46L35, Operator Algebras (math.OA)

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