Chein Automorphisms of Free Metabelian Anticommutative Algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915671438262272 |
|---|---|
| author | Nauryzbaev, Ruslan Shestakov, Ivan Umirbaev, Ualbai |
| author_facet | Nauryzbaev, Ruslan Shestakov, Ivan Umirbaev, Ualbai |
| contents | 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 $n\geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chein Automorphisms of Free Metabelian Anticommutative Algebras Nauryzbaev, Ruslan Shestakov, Ivan Umirbaev, Ualbai Rings and Algebras 17A36, 17A50, 17A30, 16S10 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 $n\geq 3$. |
| title | Chein Automorphisms of Free Metabelian Anticommutative Algebras |
| topic | Rings and Algebras 17A36, 17A50, 17A30, 16S10 |
| url | https://arxiv.org/abs/2512.11688 |