A criterion for Leavitt path algebras having invariant basis number

TL;DR

This paper establishes a matrix-theoretic criterion to determine when Leavitt path algebras of finite graphs possess the Invariant Basis Number property, and applies it to Cohn path algebras and specific graph classes.

Contribution

It introduces a new matrix-based criterion for Invariant Basis Number in Leavitt path algebras of finite graphs, expanding understanding of algebraic properties linked to graph structures.

Findings

Leavitt path algebra of a finite graph has IBN if a certain matrix condition is met.

Cohn path algebra of a finite graph also has IBN.

Identifies classes of finite graphs where Leavitt path algebras have IBN.

Abstract

In this paper, we give a matrix-theoretic criterion for the Leavitt path algebra of a finite graph has Invariant Basis Number. Consequently, we show that the Cohn path algebra of a finite graph has Invariant Basis Number, as well as provide some certain classes of finite graphs for which Leavitt path algebras having Invariant Basis Number.