2013/09/18 by Shawn McCann, McCann, Shawn
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1309.4786
openalex publication_date 2013/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver Q is a C^*-correspondence, and in turn, a Cuntz-Pimsner algebra C^*(Q). Given Γ a locally compact group and α and β endomorphisms on Γ, one may construct a topological quiver Qα,β(Γ) with vertex set Γ, and edge set Ωα,β(Γ)= \(x,y)∈Γ×Γ‖ α(y)=β(x)\. In \citeMc1, the author examined the Cuntz-Pimsner algebra \calOα,β(Γ):=C^*(Qα,β(Γ)) and found generators (and their relations) of \calOα,β(Γ). In this paper, the author translates a known criterion for simplicity of topological quivers into a precise criterion for the simplicity of topological group relations.