Dynamical comparison and Z-stability for crossed products of simple C-algebras

Eusebio Gardella, Shirly Geffen, Petr Naryshkin, Andrea Vaccaro

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We establish Z-stability for crossed products of outer actions of amenable groups on Z-stable C-algebras under a mild technical assumption which we call McDuff property with respect to invariant traces. We obtain such result using a weak form of dynamical comparison, which we verify in great generality. We complement our results by proving that McDuffness with respect to invariant traces is automatic in many cases of interest. This is the case, for instance, for every action of an amenable group G on a classifiable C-algebra A whose trace space T(A) is a Bauer simplex with finite dimensional boundary ∂eT(A), and such that the induced action G↷∂eT(A) is free. If G=Zd and the action G↷∂eT(A) is free and minimal, then we obtain McDuffness with respect to invariant traces, and thus Z-stability of the corresponding crossed product, also in case ∂eT(A) has infinite covering dimension.

Original languageEnglish
Article number109471
JournalAdvances in Mathematics
Volume438
DOIs
StatePublished - 1 Feb 2024
Externally publishedYes

Keywords

  • C-algebras
  • Classification
  • Crossed products
  • Group actions
  • Uniform Rokhlin property
  • Z-stability

ASJC Scopus subject areas

  • General Mathematics

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