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On the embedding of left-symmetric algebras into differential perm-algebras
Published 1 Jun 2021 in math.RA | (2106.00367v1)
Abstract: 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.
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