Efficient Presentations of Relative Cuntz-Krieger Algebras

Abstract

In this article, we present a new method to study relative Cuntz-Krieger algebras for higher-rank graphs. We only work with edges rather than paths of arbitrary degrees. We then use this method to simplify the existing results about relative Cuntz-Krieger algebras. We also give applications to study ideals and quotients of Toeplitz algebras.

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Acknowledgements

The authors would like to thank Iain Raeburn for sharing his insights. We are also grateful for the improvements suggested by the anonymous referee.

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Correspondence to L. O. Clark.

Additional information

This research was supported by Marsden grant 15-UOO-071 from the Royal Society of New Zealand.

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Clark, L.O., Pangalela, Y.E.P. Efficient Presentations of Relative Cuntz-Krieger Algebras. Anal Math 47, 37–65 (2021). https://doi.org/10.1007/s10476-021-0066-x

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Key words and phrases

  • higher-rank graph
  • relative graph algebra
  • graph C*-algebra

Mathematics Subject Classification

  • 46L05