## Rocky Mountain Journal of Mathematics

### Continuous-trace $k$-graph $C^*$-algebras

Danny Crytser

#### 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. A characterization of continuous-trace AF $C^*$-algebras is obtained. Partial results are given to characterize higher-rank graphs that yield $C^*$-algebras with continuous trace.

#### Article information

Source
Rocky Mountain J. Math., Volume 48, Number 5 (2018), 1511-1535.

Dates
First available in Project Euclid: 19 October 2018

https://projecteuclid.org/euclid.rmjm/1539936034

Digital Object Identifier
doi:10.1216/RMJ-2018-48-5-1511

Mathematical Reviews number (MathSciNet)
MR3866557

Zentralblatt MATH identifier
06958790

Keywords
$C^*$-algebras graphs groupoids

#### Citation

Crytser, Danny. Continuous-trace $k$-graph $C^*$-algebras. Rocky Mountain J. Math. 48 (2018), no. 5, 1511--1535. doi:10.1216/RMJ-2018-48-5-1511. https://projecteuclid.org/euclid.rmjm/1539936034

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