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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 n3n\geq 3 over a field KK 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=2n=2 are linear, and that the simplest non elementary Chein automorphism of degree 33 is absolutely wild for all n3n\geq 3.

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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