Cohn path algebras of higher-rank graphs

Abstract

In this article, we introduce Cohn path algebras of higher-rank graphs. We prove that for a higher-rank graph $\Lambda$, there exists a higher-rank graph $T\Lambda$ such that the Cohn path algebra of $\Lambda$ is isomorphic to the Kumjian-Pask algebra of $T\Lambda$. We then use this isomorphism and properties of Kumjian-Pask algebras to study Cohn path algebras. This includes proving a uniqueness theorem for Cohn path algebras.