Non-stable K-theory for Leavitt path algebras

TL;DR

This paper computes the monoid of finitely generated projective modules for Leavitt path algebras over arbitrary graphs, extending previous results to more general graph types.

Contribution

It generalizes the computation of the monoid of projective modules from countable row-finite graphs to arbitrary directed graphs.

Findings

Monoid of projective modules computed for all directed graphs

Generalization of previous results to broader class of graphs

Provides a unified framework for Leavitt path algebra modules

Abstract

We compute the monoid of isomorphism classes of finitely generated projective modules of a Leavitt path algebra over an arbitrary directed graph. Our result generalizes the result of Ara, Moreno, and Pardo in which they computed this monoid of a Leavitt path algebra over a countable row-finite directed graph.