An Anick type wild automorphism of free Poisson algebras

TL;DR

This paper constructs a specific wild automorphism in a free Poisson algebra that becomes tame when viewed as a polynomial algebra, and proves its stable tameness, advancing understanding of automorphism structures.

Contribution

It introduces an Anick type wild automorphism in free Poisson algebras and demonstrates its stable tameness, a novel finding in algebraic automorphism theory.

Findings

Constructed a wild automorphism in free Poisson algebra

Automorphism becomes tame in polynomial algebra

Proved the automorphism is stably tame

Abstract

We construct an Anick type wild automorphism $\delta$ in a 3-generated free Poisson algebra which induces a tame automorphism in a 3-generated polynomial algebra. We also show that $\delta$ is stably tame. Dedicated to the memory of professor V.A.Roman'kov