On the Lie-solvability of Novikov algebras

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Tulenbaev K., Umirbaev U., Zhelyabin V.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.22, sa.5, 2023 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 5
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1142/s0219498823501177
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Novikov algebra, Lie-solvability, nilpotency
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Süleyman Demirel Üniversitesi Adresli: Hayır

Özet

We prove that any Novikov algebra over a field of characteristic not equal 2 is Lie-solvable if and only if its commutator ideal [N, N] is right nilpotent. We also construct examples of infinite-dimensional Lie-solvable Novikov algebras N with non-nilpotent commutator ideal [N, N].