The image of Lie polynomials on real Lie algebras of dimension up to 3
Journal of Algebra, vol.659, pp.344-360, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 659
- Publication Date: 2024
- Doi Number: 10.1016/j.jalgebra.2024.07.006
- Journal Name: Journal of Algebra
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Page Numbers: pp.344-360
- Keywords: Images of polynomials, Lie algebras
- Çukurova University Affiliated: No
Abstract
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.