Higher rank graph C*-algebras

2000/07/05 by Alex Kumjian, David Pask
Mathematics · #math.OA #math.CT #msc:46L05 #msc:46L55

paper · pdf

published as New York J. Math. 6 (2000), 1-20 · 14 pages, see also http://nyjm.albany.edu:8000/j/2000/6-1nf.htm

arxiv created 2000/07/05 · arxiv updated 2009/11/30

Abstract

Building on recent work of Robertson and Steger, we associate a C*-algebra to a combinatorial object which may be thought of as a higher rank graph. This C*-algebra is shown to be isomorphic to that of the associated path groupoid. Sufficient conditions on the higher rank graph are found for the associated C*-algebra to be simple, purely infinite and AF. Results concerning the structure of crossed products by certain natural actions of discrete groups are obtained; a technique for constructing rank 2 graphs from ``commuting'' rank 1 graphs is given.

Related

• Categorising the operator algebras of groupoids and higher-rank graphs
• Embeddability of higher-rank graphs in groupoids, and the structure of their C*-algebras
• Realising the C*-algebra of a higher-rank graph as an Exel crossed product
• Topological higher-rank graphs and the C^*-algebras of topological 1-graphs
• Groupoids and C*-algebras for categories of paths