On simplicity of intermediate C*-algebras

2018/09/17 by Tattwamasi Amrutam, Amrutam, Tattwamasi, Mehrdad Kalantar +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1809.05995

arxiv created 2018/09/17 · openalex publication_date 2018/09/17 · arxiv updated 2018/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove simplicity of all intermediate C^*-algebras C^*_r(Γ)⊆ B ⊆ Γ\ltimes_r C(X) in the case of minimal actions of C^*-simple groups Γ on compact spaces X. For this, we use the notion of stationary states, recently introduced by Hartman and Kalantar (arXiv:1712.10133v2). We show that the Powers' averaging property holds for the reduced crossed product Γ\ltimes_r A for any action Γ\curvearrowright A of a C^*-simple group Γ on a unital C^*-algebra A, and use it to prove a one-to-one correspondence between stationary states on A and those on Γ\ltimes_r A.

Citations

• Stationary C*-dynamical systems
• A new look at C*-simplicity and the unique trace property of a group

Cited by

• On the inclusion \cO₂ ⊂ \cQ₂
• Unique Pseudo-Expectations for Dynamical C^*-Inclusions

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