Chein Automorphisms of Free Metabelian Anticommutative Algebras
Rings and Algebras
2025-12-15 v1
Abstract
We describe all automorphisms of a free metabelian anticommutative algebra of rank over a field 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 are linear, and that the simplest non elementary Chein automorphism of degree is absolutely wild for all .
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Cite
@article{arxiv.2512.11688,
title = {Chein Automorphisms of Free Metabelian Anticommutative Algebras},
author = {Ruslan Nauryzbaev and Ivan Shestakov and Ualbai Umirbaev},
journal= {arXiv preprint arXiv:2512.11688},
year = {2025}
}
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12 pages