Normalisation of a Poisson algebra is Poisson

TL;DR

This paper proves that the integral closure of a Poisson algebra over a field of characteristic zero retains its Poisson algebra structure, establishing a key property of Poisson algebras in algebraic geometry.

Contribution

It demonstrates that the integral closure of a Poisson algebra is itself a Poisson algebra, a result previously unestablished.

Findings

Integral closure of a Poisson algebra is Poisson

Preservation of Poisson structure under integral closure

Advances understanding of Poisson algebra properties

Abstract

We prove that the integral closure of a Poisson algebra $A$ over a field of characteristic 0 is again a Poisson algebra.