On Intermediate C^*-subalgebras of C^*-simple Group Actions

2018/11/28 by Tattwamasi Amrutam, Amrutam, Tattwamasi
Materials Science · Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Organic and Molecular Conductors Research #Spectral Theory in Mathematical Physics #math.OA

paper · pdf · doi:10.48550/arxiv.1811.11381

We have added more examples of plump subgroups, in particular showed that every non-elementary subgroup of a non-torsion convergence group is plump. We have also proved a similar result in von Neumann algebraic setting. This version also includes an appendix with Yongle Jiang containing an example of a faithful action of a $C^*$-simple group, for which every intermediate $C^*$-algebra splits

openalex publication_date 2018/11/28 · arxiv created 2019/02/06 · arxiv updated 2019/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for a large class of actions Γ\curvearrowright A of C^*-simple groups Γ on unital C^*-algebras A, including any non-faithful action of a hyperbolic group with trivial amenable radical, every intermediate C^*-subalgebra B, C_λ^*(Γ)⊆ B ⊆ A\rtimes_rΓ, is of the form A₁\rtimes_rΓ, where A₁ is a unital Γ-C^*-subalgebra of A.

Citations

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

Related

• On simplicity of intermediate C*-algebras
• Intermediate crossed product C^*-algebras
• Invariant subalgebras of the reduced group C^*-algebra
• Non-Abelian Factors for Actions of ℤ and Other Non-C^*-Simple Groups
• Inclusions of C^*-algebras arising from fixed-point algebras