2025/12/12 by Nauryzbaev, Ruslan, Shestakov, Ivan, Umirbaev, Ualbai
Mathematics · #16S10 #17A30 #17A36 #17A50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2512.11688
openalex publication_date 2025/12/12 · openalex created_date 2025/12/16 · openalex updated_date 2026/07/28
We describe all automorphisms of a free metabelian anticommutative algebra of rank n≥ 3 over a field K that move only one variable while fixing the others. Such automorphisms are called Chein automorphisms in the cases of free metabelian groups and free metabelian Lie algebras. We show that all automorphisms of a free metabelian anticommutative algebra of rank n=2 are linear, and that the simplest non elementary Chein automorphism of degree 3 is absolutely wild for all n≥ 3.