Higher rank graph C*-algebras

Details Higher rank graph C*-algebras Higher rank graph C*-algebras

2000-07-05

arxiv.org/abs/math/0007029v1

New York J. Math. 6 (2000), 1-20

Mathematics

Operator Algebras

14 pages, see also http://nyjm.albany.edu:8000/j/2000/6-1nf.htm

Scientific paper

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.

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