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Higher rank graph C*-algebras

Alex Kumjian·David Pask
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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.

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Alex Kumjian, David Pask. 2000-07-05. Higher rank graph C*-algebras. https://arxiv.org/abs/math/0007029

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