Cohn path algebras of higher-rank graphs

TL;DR

This paper introduces Cohn path algebras for higher-rank graphs, establishing an isomorphism with Kumjian-Pask algebras of related graphs, and uses this to analyze their properties including a uniqueness theorem.

Contribution

It defines Cohn path algebras for higher-rank graphs and proves an isomorphism with Kumjian-Pask algebras, enabling new analysis of their structure.

Findings

Established an isomorphism between Cohn path algebras and Kumjian-Pask algebras for higher-rank graphs.

Proved a uniqueness theorem for Cohn path algebras.

Provided new tools for studying higher-rank graph algebras.

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.