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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The cycline subalgebra of a Kumjian-Pask algebra
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by Lisa Orloff Clark, Cristóbal Gil Canto and Alireza Nasr-Isfahani PDF
Proc. Amer. Math. Soc. 145 (2017), 1969-1980 Request permission

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
  • 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
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 1969-1980
  • MSC (2010): Primary 16S10
  • DOI: https://doi.org/10.1090/proc/13439
  • MathSciNet review: 3611313