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

2022

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DOI 10.1080/00927872.2022.2028798
Data confidence 70 medium
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Abstract

Given an associative algebra satisfying the left commutativity identity abc = bac (Perm-algebra) with a derivation d, the new operation a°b=ad(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.