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

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