Rokhlin-Type Properties, Approximate Innerness and Z-Stability

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Abstract

We investigate connections between actions on separable C*-algebras with Rokhlin-type properties and absorption of the Jiang–Su algebra Z. We show that if A admits an approximately inner group action with finite Rokhlin dimension with commuting towers then A is Z-stable. We obtain analogous results for tracial version of the Rokhlin property and approximate innerness. Going beyond approximate innerness, for actions of a single automorphism which have the Rokhlin property and are almost periodic in a suitable sense, the crossed product absorbs Z even when the original algebra does not.

Original languageEnglish
Pages (from-to)157-186
Number of pages30
JournalJournal of Operator Theory
Volume87
Issue number1
DOIs
StatePublished - 2022

Keywords

  • C,-algebras
  • Jiang–su algebra
  • Rokhlin dimension
  • Rokhlin property

ASJC Scopus subject areas

  • Algebra and Number Theory

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