## 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 $\mathcal {M}$.## References

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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