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The $C^*$-algebras of finitely aligned higher-rank graphs

Iain Raeburn·Aidan Sims·Trent Yeend
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Abstract

We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned $k$-graphs. This class contains in particular all row-finite $k$-graphs. The Cuntz-Krieger relations for non-row-finite $k$-graphs look significantly different from the usual ones, and this substantially complicates the analysis of the graph algebra. We prove a gauge-invariant uniqueness theorem and a Cuntz-Krieger uniqueness theorem for the $C^*$-algebras of finitely aligned $k$-graphs.

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Iain Raeburn, Aidan Sims, Trent Yeend. 2003-05-27. The $C^*$-algebras of finitely aligned higher-rank graphs. https://arxiv.org/abs/math/0305370

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