The image of Lie polynomials on real Lie algebras of dimension up to 3

Centrone L., Fındık Ş.

Journal of Algebra, cilt.659, ss.344-360, 2024 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 659
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.jalgebra.2024.07.006
  • Dergi Adı: Journal of Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.344-360
  • Anahtar Kelimeler: Images of polynomials, Lie algebras
  • Çukurova Üniversitesi Adresli: Hayır

Özet

Let Fn be the free Lie algebra over R of rank n generated by y1,…,yn, and let f∈Fn′ be a multilinear Lie polynomial contained in the commutator ideal Fn′ of Fn. In this paper, we determine the image Imf={f(w1,…,wn)|wi∈L,i=1,…,n}⊂L, for Lie algebras L of dimension ≤3, and of the Lie algebra of dimension 4 stated in a paper of Baker dating back to 1901. In all the cases studied, the L'vov-Kaplansky Conjecture has a positive answer.