2024/11/01 by Christian d’Elbée, d'Elbée, Christian
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2411.00667
We continue our study of the Wilson conjecture for ω-categorical Lie algebras and prove that ω-categorical 4-Engel Lie algebras of characteristic 3 are nilpotent. We develop a set of tools to adapt in the definable context some classical methods for studying Engel Lie algebras (Higgins, Kostrikin, Zelmanov, Vaughan-Lee, Traustason and others). We solve the case at hand by starting a systematic study of Lie algebras for which there is a k such that the principal ideal generated by any element is nilpotent of class