arXiv subjects

Ruslan Nauryzbaev

Publications and source records attributed to Ruslan Nauryzbaev.

2 recordsLinked to original sources

arXiv2025

Chein Automorphisms of Free Metabelian Anticommutative Algebras

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 $n\geq 3$.

math.RA↗

arXiv2020

On the automorphisms of a free Lie algebra of rank 3 over an integral domain

We prove that the group of tame automorphisms of a free Lie algebra (as well as of a free anticommutative algebra) rank 3 over an arbitrary integral domain has the structure of an amalgamated free product. We construct an example of a wild automorphism of a free Lie algebra (as well as of a free anticommutative algebra) of rank 3 over an arbitrary Euclidean ring analogous to the Anick automorphism for free associative algebras.

math.RA↗