On the embedding of left-symmetric algebras into differential perm-algebras
Abstract
Given an associative algebra satisfying the left commutativity identity abc=bac (Perm-algebra) with a derivation d, the new operation a 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.
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