Continous-trace $k$-graph $C^*$-algebras

TL;DR

This paper characterizes directed graphs and higher-rank graphs whose associated $C^*$-algebras have continuous trace, using groupoid methods and desingularization techniques, extending known results to more general cases.

Contribution

It provides a complete characterization for row-finite graphs with no sources and extends partial results to higher-rank graphs regarding continuous trace $C^*$-algebras.

Findings

Characterization for row-finite graphs with no sources

Extension to general graphs via desingularization

Partial results for higher-rank graphs

Abstract

A characterization is given for directed graphs that yield graph $C^*$-algebras with continuous trace. This is established for row-finite graphs with no sources first using a groupoid approach, and extended to the general case via the Drinen-Tomforde desingularization. Partial results are given to characterize higher-rank graphs that yield $C^*$-algebras with continuous trace.