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

By Toke Meier Carlsen, Sooran Kang, J. Shotwell, Aidan Sims. 2013

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/627030155ed66ed1294f33f86bc8b43c4e4a0d85