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

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 $\ast .$ We study the Lie algebra $K=K(L(\Gamma ),\ast )$ of $\ast -$skew-symmetric elements and find necessary and sufficient conditions for the Lie algebra $[K,K]$ to be simple.

arXiv comment8 pages, 6 figures. arXiv admin note: text overlap with arXiv:1304.1922