Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771950 | Journal of Algebra | 2017 | 34 Pages |
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
Authors
Lisa Orloff Clark, Yosafat E.P. Pangalela,