SIMPLICITY CRITERION FOR C∗-ALGEBRAS ASSOCIATED WITH TOPOLOGICAL GROUP QUIVERS

Abstract. 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 [12], the author examined the Cuntz-Pimsner algebra Oα,β(Γ): = C∗(Qα,β(Γ)) and found generators (and their relations) of Oα,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