Generic classification of the quasi-free flows on the Cuntz algebra O₂

2025/08/31 by Robert Neagu, Neagu, Robert
Mathematics · #46L40 #46L55 #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2509.00829

openalex publication_date 2025/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we show that the quasi-free flows on the Cuntz algebra O₂ are generically classifiable by the inverse temperature of their unique KMS state. Along the way, we show that a large class of quasi-free flows on the Cuntz algebra O_n are generically equivariantly Z-stable and their corresponding dual action has the Rokhlin property generically.

Citations

• On a Rokhlin property for abelian group actions on C^*-algebras
• The dynamical Kirchberg-Phillips theorem
• The stable uniqueness theorem for equivariant Kasparov theory
• KK-theory of circle actions with the Rokhlin property
• Rohlin flows on von Neumann algebras
• Classification of inductive limits of 1-dimensional NCCW complexes
• Strongly self-absorbing C*-algebras
• Representation Theory and Numerical AF-invariants: The representations and centralizers of certain states on O_d
• Trace acaling automorphisms of certain stable AF algebras II

Related

• Rohlin flows on the Cuntz algebra O_∞
• Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras
• On the possible temperatures for flows on an AF algebra
• Equilibria when the temperature goes to zero
• A class of simple C^*-algebras arising from certain nonsofic subshifts