A note on the quasi-local algebra of expander graphs

2025/08/10 by Bruno M. Braga, Braga, Bruno M., Ján Špakula +3
Mathematics · #46L05 05C48 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2508.07327

openalex publication_date 2025/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the quasi-local algebra of a coarse disjoint union of expander graphs does not contain a Cartan subalgebra isomorphic to ℓ_∞. N. Ozawa has recently shown that these algebras are distinct from the uniform Roe algebras of expander graphs, and our result describes a further difference.

Citations

• A rigidity framework for Roe-like algebras
• Embeddings of matrix algebras into uniform Roe algebras and quasi-local algebras
• Coarse equivalence versus bijective coarse equivalence of expander graphs
• Embeddings of von Neumann algebras into uniform Roe algebras and quasi-local algebras
• On the structure of asymptotic expanders
• Quasi-local Algebras and Asymptotic Expanders
• Quasi-Locality and Property A
• Index theorems for uniformly elliptic operators
• Indices of pseudodifferential operators on open manifolds
• On Rigidity of Roe algebras

Related

• Coarse equivalence versus bijective coarse equivalence of expander graphs
• Quasi-local Algebras and Asymptotic Expanders
• A note on the structure of expanders
• Non-K-exact uniform Roe C*-algebras
• Remarks on partitions into expanders