## Abstract

Let

trace space T(

(2) α ⊗ id

(3) α ⊗ id

conjugate to α ⊗ id

*A*be a separable, unital, simple,*Z*-stable, nuclear*C*^{∗}-algebra, and let α:*G*→ Aut(*A*) be an action of a countable amenable group. If thetrace space T(

*A*) is a Bauer simplex and the action of G on ∂e*T*(*A*) has finite orbits and Hausdorff orbit space, we show that the following are equivalent: (1) α is strongly outer;(2) α ⊗ id

_{Z}has the weak tracial Rokhlin property. If G is moreover residually finite, the above conditions are also equivalent to(3) α ⊗ id

_{Z}has finite Rokhlin dimension (in fact, at most 2). When the covering dimension of ∂eT(A) is finite, we prove that α is cocycleconjugate to α ⊗ id

_{Z}. In particular, the equivalences above hold for α in place of α ⊗ id_{Z}Original language | English |
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State | Published - 2018 |

### Publication series

Name | Arxiv preprint |
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## Keywords

- Mathematics - Operator Algebras
- Mathematics - Functional Analysis