The V-monoid of a weighted Leavitt path algebra

TL;DR

This paper accurately computes the V-monoid of weighted Leavitt path algebras for row-finite graphs, correcting previous errors and confirming existing K_0 descriptions.

Contribution

It provides the first correct computation of the V-monoid for weighted Leavitt path algebras, rectifying prior inaccuracies in the literature.

Findings

Corrected the V-monoid computation for weighted Leavitt path algebras

Confirmed the existing K_0 description as accurate

Clarified the relationship between V-monoid and K_0 in this context

Abstract

We compute the $V$-monoid of a weighted Leavitt path algebra of a row-finite weighted graph, correcting a wrong computation of the $V$-monoid that exists in the literature. Further we show that the description of $K_0$ of a weighted Leavitt path algebra that exists in the literature is correct (although the computation was based on a wrong $V$-monoid description).