Article ID Journal Published Year Pages File Type
5771950 Journal of Algebra 2017 34 Pages PDF
Abstract
We extend the definition of Kumjian-Pask algebras to include algebras associated to finitely aligned higher-rank graphs. We show that these Kumjian-Pask algebras are universally defined and have a graded uniqueness theorem. We also prove the Cuntz-Krieger uniqueness theorem; to do this, we use a groupoid approach. As a consequence of the graded uniqueness theorem, we show that every Kumjian-Pask algebra is isomorphic to the Steinberg algebra associated to its boundary path groupoid. We then use Steinberg algebra results to prove the Cuntz-Krieger uniqueness theorem and also to characterize simplicity and basic simplicity.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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