On the simplicity of Lie algebra of Leavitt path algebra

TL;DR

This paper characterizes when the Lie algebra derived from a Leavitt path algebra of a row-finite graph is simple, providing a complete set of necessary and sufficient conditions.

Contribution

It establishes a full characterization of simplicity for the Lie algebra associated with Leavitt path algebras of row-finite graphs.

Findings

Identifies necessary and sufficient conditions for Lie algebra simplicity.

Provides a complete classification based on graph properties.

Advances understanding of algebraic structures related to graph algebras.

Abstract

For a field $F$ and a row-finite directed graph $\Gamma$ let $L(\Gamma)$ be the Leavitt path algebra. We find necessary and sufficient conditions for the Lie algebra $[L(\Gamma),L(\Gamma)]$ to be simple.