Work

The cycline subalgebra of a Kumjian-Pask algebra

Year: 2016

Type: article

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 $\mathcal {M}$.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/13439

Authors: Lisa Orloff Clark, Cristóbal Gil Canto, Alireza Nasr-Isfahani

Institutions: University of Otago, Universidad de Málaga, University of Isfahan, Institute for Research in Fundamental Sciences

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze