On the Lie-solvability of Novikov algebras


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Tulenbaev K., Umirbaev U., Zhelyabin V.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1142/s0219498823501177
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Novikov algebra, Lie-solvability, nilpotency
  • Süleyman Demirel University Affiliated: No

Abstract

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].