On the embedding of left-symmetric algebras into differential perm-algebras

Given an associative algebra satisfying the left commutativity identity $abc=bac$ (Perm-algebra) with a derivation $d$, the new operation $a\circ b = a d(b)$ is left-symmetric (pre-Lie). We derive necessary and sufficient conditions for a left-symmetric algebra to be embeddable into a differential Perm-algebra.