2015/12/21 by Clark, Lisa Orloff, Pangalela, Yosafat E. P. · 5 citations
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1512.06547
We extend the 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-Kreiger 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-Kreiger uniqueness theorem and also to characterize simplicity and basic simplicity.