Stabilising uniform property Gamma

TL;DR

This paper introduces stabilised property Gamma, a new invariant for C*-algebras, and demonstrates its role in characterizing when certain nuclear C*-algebras absorb the Jiang-Su algebra tensorially.

Contribution

The paper defines stabilised property Gamma and proves its invariance under stable isomorphism, linking it to Z-stability in nuclear C*-algebras.

Findings

Stabilised property Gamma is invariant under stable isomorphism.

Simple separable nuclear C*-algebras with this property absorb the Jiang-Su algebra.

Establishes a criterion for Z-stability involving stabilised property Gamma.

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.