#### Title

The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources

#### RIS ID

86671

#### Abstract

We catalogue the primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources. Each maximal tail in the vertex set has an abelian periodicity group of finite rank at most that of the graph; the primitive ideals in the Cuntz–Krieger algebra are indexed by pairs consisting of a maximal tail and a character of its periodicity group. The Cuntz–Krieger algebra is primitive if and only if the whole vertex set is a maximal tail and the graph is aperiodic.

## Publication Details

Carlsen, T. Meier., Kang, S., Shotwell, J. & Sims, A. (2014). The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources. Journal of Functional Analysis, 266 (4), 2570-2589.