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

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Kolesnikov P. S. , Sartayev B. K.

COMMUNICATIONS IN ALGEBRA, vol.50, no.8, pp.3246-3260, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 8
  • Publication Date: 2022
  • Doi Number: 10.1080/00927872.2022.2028798
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.3246-3260
  • Keywords: Left-symmetric algebra, derivation, identity, Novikov algebra, dialgebra, ROTA-BAXTER
  • Süleyman Demirel University Affiliated: No

Abstract

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