2024/08/16 by Tattwamasi Amrutam, Amrutam, Tattwamasi, Yongle Jiang +1 · 1 citation
Computer Science · Mathematics · #46L06 #46L45 #Computational Physics and Python Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Parallel Computing and Optimization Techniques #Primary 46M05 #Secondary 37B05 #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2408.08635
openalex publication_date 2024/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a discrete group. Given unital G-C^*-algebras A and B, we give an abstract condition under which every G-subalgebra C of the form A⊂ C⊂ A⊗minB is a tensor product. This generalizes the well-known splitting results in the context of C^*-algebras by Zacharias and Zsido. As an application, we prove a topological version of the Intermediate Factor theorem. When a product group G=Γ1×Γ2 acts (by a product action) on the product of corresponding Γi-boundaries ∂Γi, using the abstract condition, we show that every intermediate subalgebra C(X)\subsetC⊂ C(X)⊗minC(∂Γ1× ∂Γ2) is a tensor product (under some additional assumptions on X). This can be considered as a topological version of the Intermediate Factor theorem. We prove that our assumptions are necessary and cannot generally be relaxed. We also introduce the notion of a uniformly rigid action for C^*-algebras and use it to give various classes of inclusions A⊂ A⊗minB for which every invariant intermediate algebra is a tensor product.