A wild automorphism of a free Novikov algebra

TL;DR

This paper constructs explicit examples of a wild exponential automorphism and a non-triangulable locally nilpotent derivation in the free Novikov algebra with three variables, illustrating complex automorphism behavior.

Contribution

It provides the first known examples of wild automorphisms and non-triangulable derivations in free Novikov algebras, advancing understanding of their automorphism groups.

Findings

Constructed a wild exponential automorphism of the free Novikov algebra

Presented a non-triangulable locally nilpotent derivation in the same algebra

Demonstrated complex automorphism structures in free Novikov algebras

Abstract

An example of a non-triangulable locally nilpotent derivation and an example of a wild exponential automorphism of the free Novikov algebra $N\left\langle x,y,z\right\rangle$ in three variables $x,y,z$ over a field of characteristic zero are constructed.