Amenable actions on finite simple C*-algebras arising from flows on Pimsner algebras

2023/05/22 by Suzuki, Yuhei
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Primary 46L55 #Secondary 46L35

paper · doi:10.48550/arxiv.2305.13056

Abstract

Associated to a family of G-∗-endomorphisms on a G-C*-algebra A satisfying certain minimality conditions, we give a G-C*-correspondence E over A whose Cuntz--Pimsner algebra O_E is simple. For certain quasi-free flows γ (commuting with the G-action) on O_E, we further prove the simplicity of the reduced crossed product O_E \rtimes_γℝ. We then classify the KMS weights of γ. This in particular gives a sufficient condition for O_E and O_E\rtimes_γℝ to be stably finite (and to be stably projectionless). As the amenability of G \curvearrowright A inherits to the induced actions G \curvearrowright O_E, O_E\rtimes_γℝ, this provides a new systematic framework to provide amenable actions on stably finite simple C*-algebras.

Related

• Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras
• Every countable group admits amenable actions on stably finite simple C*-algebras
• Injectivity, crossed products, and amenable group actions
• Groupoid actions on C^*-correspondences
• Dynamical comparison and Z-stability for crossed products of simple C^*-algebras