Simplicity of the Lie algebra of skew symmetric elements of a Leavitt path algebra

TL;DR

This paper investigates the Lie algebra formed by skew-symmetric elements in Leavitt path algebras, providing conditions under which the derived Lie algebra is simple, thus advancing understanding of algebraic structures related to graph algebras.

Contribution

It characterizes when the Lie algebra of skew-symmetric elements in Leavitt path algebras is simple, offering new insights into their algebraic structure.

Findings

Necessary and sufficient conditions for simplicity of [K,K]

Characterization of the Lie algebra of skew-symmetric elements

Advancement in understanding Leavitt path algebra structures

Abstract

For a field $F$ of characteristic not 2 and a directed row-finite graph $\Gamma$ let $L(\Gamma)$ be the Leavitt path algebra with the standard involution $*.$ We study the Lie algebra $K=K(L(\Gamma),*)$ of $*-$skew-symmetric elements and find necessary and sufficient conditions for the Lie algebra $[K,K]$ to be simple.