Simple Lie algebras arising from Leavitt path algebras

For a field K and directed graph E, we analyze those elements of the Leavitt path algebra LK(E) which lie in the commutator subspace [LK(E),LK(E)]. This analysis allows us to give easily computable necessary and sufficient conditions to determine which Lie algebras of the form [LK(E),LK(E)] are simple, when E is row-finite (i.e., has finite out-degree) and LK(E) is simple.