# Weighted Leavitt path algebras that are isomorphic to unweighted Leavitt path algebras

## TL;DR

This paper characterizes when weighted Leavitt path algebras are isomorphic to unweighted ones, showing that certain finiteness and regularity conditions imply isomorphism to unweighted algebras.

## Contribution

It provides a complete characterization of weighted graphs whose Leavitt path algebras are isomorphic to unweighted cases, extending understanding of algebraic structures.

## Key findings

- Weighted Leavitt path algebra isomorphism characterized by graph properties
- Locally finite, Noetherian, Artinian, von Neumann regular, finite Gelfand-Kirillov dimension imply isomorphism
- Conditions under which weighted algebras reduce to unweighted Leavitt path algebras

## Abstract

Let $K$ be a field. We characterise the row-finite weighted graphs $(E,w)$ such that the weighted Leavitt path algebra $L_K(E,w)$ is isomorphic to an unweighted Leavitt path algebra. Moreover, we prove that if $L_K(E,w)$ is locally finite, or Noetherian, or Artinian, or von Neumann regular, or has finite Gelfand-Kirillov dimension, then $L_K(E,w)$ is isomorphic to an unweighted Leavitt path algebra.