2013/04/23 by Lisa Orloff Clark, Clark, Lisa Orloff, Claire Flynn +3
Mathematics · #16W50 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16W50
paper · pdf · doi:10.48550/arxiv.1304.6421
Minor changes made. This version is to appear in the Journal of Algebra
arxiv created 2013/09/25 · arxiv updated 2013/09/26
The Kumjian-Pask algebra of a higher-rank graph generalises the Leavitt path algebra of a directed graph. We extend the definition of Kumjian-Pask algebra to row-finite higher-rank graphs Λ with sources which satisfy a local-convexity condition. After proving versions of the graded-uniqueness theorem and the Cuntz-Krieger uniqueness theorem, we study the Kumjian-Pask algebra of rank-2 Bratteli diagrams by studying certain finite subgraphs which are locally convex. We show that the desourcification procedure of Farthing and Webster yields a row-finite higher-rank graph Λ without sources such that the Kumjian-Pask algebras of Λ and Λ are Morita equivalent. We then use the Morita equivalence to study the ideal structure of the Kumjian-Pask algebra of Λ by pulling the appropriate results across the equivalence.