Automorphisms and derivations of free Poisson algebras in two variables

TL;DR

This paper proves that automorphisms of a free Poisson algebra in two variables are tame and that its locally nilpotent derivations are triangulable, advancing understanding of its algebraic structure.

Contribution

It establishes the tameness of automorphisms and triangulability of derivations in free Poisson algebras with two variables, a novel result in Poisson algebra theory.

Findings

Automorphisms of P are tame.

Locally nilpotent derivations of P are triangulable.

Advances understanding of algebraic structure of free Poisson algebras.

Abstract

Let P be a free Poisson algebra in two variables over a field of characteristic zero. We prove that the automorphisms of P are tame and that the locally nilpotent derivations of P are triangulable.