# Lie-Poisson structures over differential algebras

## TL;DR

This paper develops an algebraic framework for Lie-Poisson structures over differential algebras, extending Hamiltonian evolution equations to systems with constraints using Olver's approach.

## Contribution

It introduces a novel algebraic construction for Hamiltonian systems with constraints based on Olver's method.

## Key findings

- Provides a new algebraic framework for constrained Hamiltonian systems
- Extends Lie-Poisson structures to differential algebras
- Facilitates analysis of Hamiltonian evolution equations with constraints

## Abstract

In this paper we use key elements of the Olver's approach to Hamiltonian evolution equations in partial derivatives and propose an algebraic construction appropriate for Hamiltonian evolution systems with constraints.