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Vol. 51 No. 3–4 (2025)
Serdica Mathematical Journal

Articles

Chein automorphisms of free metabelian anticommutative algebras

https://doi.org/10.55630/serdica.2025.51.351-366

Published 23-12-2025

  • Ruslan Nauryzbaev
    • ,
  • Ivan Shestakov
    • ,
  • Ualbai Umirbaev

Ruslan Nauryzbaev
L. N. Gumilyov Eurasian National University

Ivan Shestakov
Shenzhen International Center for Mathematics, China and Universidade de São Paulo, Brazil

Ualbai Umirbaev
Wayne State University, USA and Institute of Mathematics and Mathematical Modeling, Kazakhstan

Abstract

We describe all automorphisms of a free metabelian anticommutative algebra of rank \(n\geq 3\) 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 \(n\geq 3\).

2020 Mathematics Subject Classification:

17A36, 17A50, 17A30, 16S10

Keywords

automorphism, derivation, metabelian algebra, anticommutative algebra, divergence

Full text

Author Details

Ruslan Nauryzbaev

Department of Mathematics
L. N. Gumilyov Eurasian National University
Astana, Kazakhstan
e-mail: nauryzbaevr@gmail.com

Ivan Shestakov

Shenzhen International Center for Mathematics
Shenzhen, China
and
Instituto de Matemática e Estatística
Universidade de São Paulo, Brazil
e-mail: shestak@ime.usp.br

Ualbai Umirbaev

Department of Mathematics
Wayne State University
Detroit, USA
and
Institute of Mathematics and Mathematical Modeling
Almaty, Kazakhstan
e-mail: umirbaev@wayne.edu

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