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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Kumjian-Pask algebras of higher-rank graphs


Authors: Gonzalo Aranda Pino, John Clark, Astrid an Huef and Iain Raeburn
Journal: Trans. Amer. Math. Soc. 365 (2013), 3613-3641
MSC (2010): Primary 16W50; Secondary 46L05
Published electronically: February 28, 2013
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Abstract: We introduce higher-rank analogues of the Leavitt path algebras, which we call the Kumjian-Pask algebras. We prove graded and Cuntz-Krieger uniqueness theorems for these algebras, and analyze their ideal structure.


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Additional Information

Gonzalo Aranda Pino
Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, 29071 Málaga, Spain
Email: g.aranda@uma.es

John Clark
Affiliation: Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand
Email: jclark@maths.otago.ac.nz

Astrid an Huef
Affiliation: Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand
Email: astrid@maths.otago.ac.nz

Iain Raeburn
Affiliation: Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand
Email: iraeburn@maths.otago.ac.nz

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05717-0
PII: S 0002-9947(2013)05717-0
Keywords: Leavitt path algebra, Cuntz-Krieger algebra, higher-rank graph, graph algebra
Received by editor(s): June 21, 2011
Received by editor(s) in revised form: October 4, 2011
Published electronically: February 28, 2013
Additional Notes: The results in this paper were obtained during a working seminar at the University of Otago. The authors thank the other participants for their comments and input, and especially Jon Brown, Iain Dangerfield and Robbie Hazlewood.
Article copyright: © Copyright 2013 American Mathematical Society