Weighted Leavitt Path Algebras that are Isomorphic 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 LK(E, w) is isomorphic to an unweighted Leavitt path algebra. Moreover, we prove that if LK(E, w) is locally finite, or Noetherian, or Artinian, or von Neumann regular, or has finite Gelfand-Kirillov dimension, then LK(E, w) is isomorphic to an unweighted Leavitt path algebra.