Rokhlin-type properties, approximate innerness and Z-stability
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Published:2021-12-15
Issue:1
Volume:87
Page:157-186
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ISSN:0379-4024
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Container-title:Journal of Operator Theory
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language:
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Short-container-title:J. Operator Theory
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.
Publisher
Theta Foundation
Subject
Algebra and Number Theory
Cited by
1 articles.
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