STRONGLY OUTER ACTIONS OF AMENABLE GROUPS ON Z-STABLE C-ALGEBRAS

Eusebio Gardella, Ilan Hirshberg

Research output: Working paper/PreprintPreprint

Abstract

Let 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 the
trace space T(A) is a Bauer simplex and the action of G on ∂eT(A) has finite orbits and Hausdorff orbit space, we show that the following are equivalent: (1) α is strongly outer;
(2) α ⊗ idZ has the weak tracial Rokhlin property. If G is moreover residually finite, the above conditions are also equivalent to
(3) α ⊗ idZ has finite Rokhlin dimension (in fact, at most 2). When the covering dimension of ∂eT(A) is finite, we prove that α is cocycle
conjugate to α ⊗ idZ . In particular, the equivalences above hold for α in place of α ⊗ idZ
Original languageEnglish
StatePublished - 2018

Publication series

NameArxiv preprint

Keywords

  • Mathematics - Operator Algebras
  • Mathematics - Functional Analysis

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