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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The cycline subalgebra of a Kumjian-Pask algebra


Authors: Lisa Orloff Clark, Cristóbal Gil Canto and Alireza Nasr-Isfahani
Journal: Proc. Amer. Math. Soc. 145 (2017), 1969-1980
MSC (2010): Primary 16S10
DOI: https://doi.org/10.1090/proc/13439
Published electronically: November 21, 2016
MathSciNet review: 3611313
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Abstract: Let $\Lambda$ be a row-finite higher-rank graph with no sources. We identify a maximal commutative subalgebra $\mathcal {M}$ inside the Kumjian-Pask algebra $\mathrm {KP}_R(\Lambda )$. We also prove a generalized Cuntz-Krieger uniqueness theorem for Kumjian-Pask algebras which says that a representation of $\mathrm {KP}_R(\Lambda )$ is injective if and only if it is injective on $\mathcal {M}$.


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Additional Information

Lisa Orloff Clark
Affiliation: Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand
MR Author ID: 624226
Email: lclark@maths.otago.ac.nz

Cristóbal Gil Canto
Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, 29071, Málaga, Spain
Email: cristogilcanto@gmail.com; cgilc@uma.es

Alireza Nasr-Isfahani
Affiliation: Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran – and – School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
MR Author ID: 634713
Email: nasr_a@sci.ui.ac.ir; nasr@ipm.ir

Keywords: Kumjian-Pask algebras, higher-rank graph, uniqueness theorem
Received by editor(s): March 2, 2016
Received by editor(s) in revised form: July 5, 2016
Published electronically: November 21, 2016
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2016 American Mathematical Society