Leavitt path algebras of labelled graphs

• DOI: 10.1016/j.jalgebra.2023.04.009
• Publication Date: 2023-04-17T15:04:32Z
• Authors: Giuliano Boava; Gilles G. de Castro; Daniel Gonçalves; Daniel W. van Wyk
• Keywords: Unital

A Leavitt labelled path algebra over a commutative unital ring is associated with a labelled space, generalizing Leavitt path algebras associated with graphs and ultragraphs as well as torsion-free commutative algebras generated by idempotents. We show that Leavitt labelled path algebras can be realized as partial skew group rings, Steinberg algebras, and Cuntz-Pimsner algebras. Via these realizations we obtain generalized uniqueness theorems, a description of diagonal preserving isomorphisms and we characterize simplicity of Leavitt labelled path algebras. In addition, we prove that a large class of partial skew group rings can be realized as Leavitt labelled path algebras.