C*-algebras associated with topological group quivers II: K-groups

2013/01/30 by McCann, Shawn J.
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1301.7347

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 Q_α,β(Γ) with vertex set Γ, and edge set Ω_α,β(Γ)= \(x,y)∈Γ×Γ\st α(y)=β(x)\. In \citeMc1, the author examined the Cuntz-Pimsner algebra \cO_α,β(Γ):=C^*(Q_α,β(Γ)) and found generators (and their relations) of \cO_α,β(Γ). In this paper, the author uses this information to create a six term exact sequence in order to calculate the K-groups of \cO_α,β(Γ).

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