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

Iain Raeburn; Aidan Sims; Trent Yeend

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

Operator Algebras 2007-05-23 v1

Authors: Iain Raeburn , Aidan Sims , Trent Yeend

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.

Keywords

c*-algebras higher-rank graphs finitely aligned k-graphs cuntz-krieger families graph algebras gauge-invariant uniqueness theorem cuntz-krieger uniqueness theorem

Cite

@article{arxiv.math/0305370,
  title  = {The $C^*$-algebras of finitely aligned higher-rank graphs},
  author = {Iain Raeburn and Aidan Sims and Trent Yeend},
  journal= {arXiv preprint arXiv:math/0305370},
  year   = {2007}
}

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27 pages

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

Abstract

Keywords

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