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

Creative Commons License

Kolesnikov P. S., Sartayev B. K.

COMMUNICATIONS IN ALGEBRA, cilt.50, sa.8, ss.3246-3260, 2022 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 8
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/00927872.2022.2028798
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.3246-3260
  • Anahtar Kelimeler: Left-symmetric algebra, derivation, identity, Novikov algebra, dialgebra, ROTA-BAXTER
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Süleyman Demirel Üniversitesi Adresli: Hayır

Özet

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.