Some notes on complex Kumjian-Pask algebras of finitely aligned k-graphs

Suppose ۸ is a finitely aligned k-graph. In this paper we present some conditions for the k-graph ۸ in order the complex Kumjian-Pask algebra KP ℂ(۸) is finite dimensional. This is an improvement for the previous results when the k-graph ۸ is row finite without sources and when ۸ is locally convex row finite k-graph. We also characterise simple Kumjian-Pask algebra KP R (۸)