On the Nowicki conjecture for the free metabelian Leibniz algebras

ÖĞÜŞLÜ N. Ş., FINDIK Ş.

Journal of Algebra and its Applications, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1142/s0219498827501866
  • Dergi Adı: Journal of Algebra and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Algebras of constants, Leibniz algebra, the Nowicki conjecture
  • Çukurova Üniversitesi Adresli: Evet

Özet

Let L be the free metabelian Leibniz algebra over a field K of characteristic zero, gen-erated by x1, x2, y1, y2. We consider the map δ(yi) = xi, δ(xi) = 0, i = 1, 2, uniquelyextended to a derivation of Leibniz algebra L. Such linear locally nilpotent derivationsare called Nowicki derivations due to his conjecture in 1994 providing a generating set forthe algebra Aδ of constants of δ in a polynomial ring A with even number of generators.This conjecture was confirmed afterwards, following different analogues of the conjec-ture studied in various noncommutative or associative algebras, so far. In this study, weinvestigate the generators of K[x1, x2, y1, y2]δ-module (L′)δ , where L′ = [L, L] is thecommutator ideal of L.