2024/04/15 by Tattwamasi Amrutam, Eli Glasner, Amrutam, Tattwamasi +3
Materials Science · Mathematics · #37A55 #37B05 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Topology (math.GT) #Operator Algebras (math.OA) #Organic and Molecular Conductors Research
paper · pdf · doi:10.48550/arxiv.2404.09803
openalex publication_date 2024/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a dynamical system (X, Γ), the corresponding crossed product C^*-algebra C(X)\rtimesrΓ is called reflecting, when every intermediate C^*-algebra C^*r(Γ)<A < C(X)\rtimesrΓ is of the form A=C(Y)\rtimesrΓ, corresponding to a dynamical factor X → Y. It is called almost reflecting if 𝔼(A) ⊂ A for every such A. These two notions coincide for groups admitting the approximation property (AP). Let Γ be a non-elementary convergence group or a lattice in SLd(ℝ) for some d ≥ 2. We show that any uniformly rigid system (X,Γ) is almost reflecting. In particular, this holds for any equicontinuous action. In the von Neumann setting, for the same groups Γ and any uniformly rigid system (X,B,μ, Γ) the crossed product algebra L∞(X,μ)\rtimesΓ is reflecting. An inclusion of algebras A\subsetB is called minimal ambient if there are no intermediate algebras. As a demonstration of our methods, we construct examples of minimal ambient inclusions with various interesting properties in the C^* and the von Neumann settings.