The Nagata automorphism of free nonassociative algebras of rank two over Eucledean domains

TL;DR

This paper constructs an analogue of the Nagata automorphism for free nonassociative and commutative algebras of rank two over Euclidean domains, demonstrating that it is a wild automorphism.

Contribution

It introduces a new automorphism in the nonassociative algebra setting and proves its wildness, extending the understanding of automorphisms in algebraic structures.

Findings

Constructed an analogue of Nagata automorphism for nonassociative algebras.

Proved the automorphism is wild, indicating complexity in the algebraic structure.

Extended the concept of wild automorphisms to nonassociative contexts.

Abstract

We construct an analogue of the Nagata automorphism of free nonassociative algebras and free commutative algebras of rank two over a Euclidean domain and prove that it is wild.