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Cohn Path Algebras of Higher-Rank Graphs

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Abstract

In this article, we introduce Cohn path algebras of higher-rank graphs. We prove that for a higher-rank graph Λ, there exists a higher-rank graph T Λ such that the Cohn path algebra of Λ is isomorphic to the Kumjian-Pask algebra of T Λ. We then use this isomorphism and properties of Kumjian-Pask algebras to study Cohn path algebras. This includes proving a uniqueness theorem for Cohn path algebras.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin, 9054, New Zealand

    Lisa Orloff Clark & Yosafat E. P. Pangalela

Authors
  1. Lisa Orloff Clark
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  2. Yosafat E. P. Pangalela
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Corresponding author

Correspondence to Yosafat E. P. Pangalela.

Additional information

Presented by Kenneth Goodearl.

This research was done as part of the second author’s PhD thesis at the University of Otago under the supervision of the first author and Iain Raeburn. Thank you to Iain for his guidance. This research was also 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. Cohn Path Algebras of Higher-Rank Graphs. Algebr Represent Theor 20, 47–70 (2017). https://doi.org/10.1007/s10468-016-9631-6

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  • DOI: https://doi.org/10.1007/s10468-016-9631-6

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