Let A be an algebraically simple, separable, nuclear, Z-stable C * -algebra for which the trace space T (A) is a Bauer simplex and the extremal boundary ∂ e T (A) has finite covering dimension. We prove that each automorphism α on A is cocycle conjugate to its tensor product with the trivial automorphism on the Jiang-Su algebra. At least for single automorphisms this generalizes a recent result by Gardella-Hirshberg. If α is strongly outer as an action of Z, we prove it has finite Rokhlin dimension with commuting towers. As a consequence it tensorially absorbs any automorphism on the Jiang-Su algebra.

No abstract

We consider the notion of equivariant uniform property Gamma for actions of countable discrete groups on C * -algebras that admit traces. In case the group is amenable and the C * -algebra has a compact tracial state space, we prove that this property implies a kind of tracial local-to-global principle for the C * -dynamical system, generalizing a recent such principle for C * -algebras exhibited in work of Castillejos et al. For actions on simple nuclear Z-stable C * -algebras, we use this to prove that equivariant uniform property Gamma is equivalent to equivariant Z-stability, generalizing a result of Gardella-Hirshberg-Vaccaro.