The classification of Rokhlin flows on C*-algebras

Abstract

We study flows on C*-algebras with the Rokhlin property. We show that every Kirchberg algebra carries a unique Rokhlin flow up to cocycle conjugacy, which confirms a long-standing conjecture of Kishimoto. We moreover present a classification theory for Rokhlin flows on C*-algebras satisfying certain technical properties, which hold for many C*-algebras covered by the Elliott program. As a consequence, we obtain the following further classification theorems for Rokhlin flows. Firstly, we extend the statement of Kishimoto's conjecture to the non-simple case: Up to cocycle conjugacy, a Rokhlin flow on a separable, nuclear, strongly purely infinite C*-algebra is uniquely determined by its induced action on the prime ideal space. Secondly, we give a complete classification of Rokhlin flows on simple classifiable $KK$-contractible C*-algebras: Two Rokhlin flows on such a C*-algebra are cocycle conjugate if and only if their induced actions on the cone of lower-semicontinuous traces are affinely conjugate.

57 pages; this version has been accepted for publication in Communications in Mathematical Physics

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• Equivariant property (SI) revisited
• On a categorical framework for classifying C*-dynamics up to cocycle conjugacy
• Equivariant property Gamma and the tracial local-to-global principle for C*-dynamics
• Equivariant Kirchberg-Phillips type absorption for the Razak-Jacelon algebra