## Rocky Mountain Journal of Mathematics

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

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

#### 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

**Permanent link to this document**

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

**Subjects**

Primary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

**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