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 Γ let L(Γ) be the Leavitt Path Algebra with standard involution *. We study the lie algebra of K = K(L(Γ), *) of * −skew-symmetric elements and find necessary and sufficient conditions for the Lie algebra [K, K] to be simple.