# Enveloping algebras of double Poisson-Ore extensions

## TL;DR

This paper proves that the Poisson enveloping algebra of a double Poisson-Ore extension can be constructed as an iterated double Ore extension, revealing invariants preserved under this process.

## Contribution

It establishes that the Poisson enveloping algebra of a double Poisson-Ore extension is an iterated double Ore extension, linking Poisson algebra structures with Ore extension theory.

## Key findings

- Poisson enveloping algebra is an iterated double Ore extension
- Invariants are preserved under iterated double Ore extensions
- Provides a new perspective on the structure of Poisson enveloping algebras

## Abstract

It is proved that the Poisson enveloping algebra of a double Poisson-Ore extension is an iterated double Ore extension. As an application, properties that are preserved under iterated double Ore extensions are invariants of the Poisson enveloping algebra of a double Poisson-Ore extension.