Bases for Kumjian-Pask algebras over standard $k$-graphs

TL;DR

This paper establishes an explicit basis for Kumjian-Pask algebras over standard $k$-graphs, enhancing understanding of their algebraic structure and facilitating further research in higher-rank graph algebras.

Contribution

It provides a concrete $R$-basis for Kumjian-Pask algebras over standard $k$-graphs, a novel result in the study of these algebraic structures.

Findings

Derived an explicit $R$-basis for $KP_R( ext{standard }k ext{-graphs})

Enhanced understanding of the algebraic structure of Kumjian-Pask algebras

Facilitated future research in higher-rank graph algebras

Abstract

For any Kumjian-Pask algebra $KP_R(\Lambda)$ defined over a $k$-graph $\Lambda$ of a special kind (a "standard $k$-graph"), we obtain an $R$-basis.