# The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras

## TL;DR

This paper introduces differential graded Poisson Hopf algebras and explores the structures on their universal enveloping algebras, extending classical Poisson Hopf algebra theory into a graded differential context.

## Contribution

It defines DG Poisson Hopf algebras and analyzes the structures of their universal enveloping algebras, providing a new framework in the field.

## Key findings

- Defined differential graded Poisson Hopf algebras
- Analyzed structures on their universal enveloping algebras
- Extended classical Poisson Hopf algebra theory

## Abstract

In this paper, the so-called differential graded (DG for short) Poisson Hopf algebra is introduced, which can be considered as a natural extension of Poisson Hopf algebras in the differential graded setting. The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras are discussed.