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

Authors

Toke Meier Carlsen, NTNUFollow
Sooran Kang, University of OtagoFollow
Jacob Shotwell, Arizona State University
Aidan Sims, University of WollongongFollow

RIS ID

86671

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.

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.