Prime and primitive Kumjian-Pask algebras

Abstract

In this paper, prime as well as primitive Kumjian-Pask algebras $\mathrm{KP}_R(\Lambda)$ of a row-finite $k$-graph $\Lambda$ over a unital commutative ring $R$ are completely characterized in graph-theoretic and algebraic terms. By applying quotient $k$-graphs, these results describe prime and primitive graded basic ideals of Kumjian-Pask algebras. In particular, when $\Lambda$ is strongly aperiodic and $R$ is a field, all prime and primitive ideals of a Kumjian-Pask algebra $\mathrm{KP}_R(\Lambda)$ are determined.