Simple modules for Kumjian-Pask algebras

Abstract

The paper introduces the notion of a representation $k$-graph $(\Delta,\alpha)$ for a given $k$-graph $\Lambda$. It is shown that any representation $k$-graph for $\Lambda$ yields a module for the Kumjian-Pask algebra $KP(\Lambda)$, and the representation $k$-graphs yielding simple modules are characterised. Moreover, the category $RG(\Lambda)$ of representation $k$-graphs for $\Lambda$ is investigated using the covering theory of higher-rank graphs.