2024/01/14 by Ualbai Umirbaev, Umirbaev, Ualbai
Mathematics · #17B01 #17B30 #17B40 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2401.07182
openalex publication_date 2024/01/14 · openalex created_date 2024/01/18 · openalex updated_date 2026/07/28
The well-known Bachmuth-Mochizuki-Roman'kov Theorem \citeBM,Romankov85 states that every automorphism of the free metabelian group of rank ≥ 4 is tame. In 1992 Yu. Bahturin and S. Nabiyev \citeBN claimed that every nontrivial inner automorphism of the free metabelian Lie algebra Mn of any rank n≥ 2 over a field of characteristic zero is wild. More examples of wild automorphisms of Mn of rank n≥ 4 were given in 2008 by Z. Özcurt and N. Ekici \citeOE. The main goal of this note is to show that both articles contain uncorrectable errors and to draw the attention of specialists to the fact that the question of tame and wild automorphisms for free metabelian Lie algebras Mn of rank n≥ 4 is still widely open.