Non-Abelian Lie algebroids over jet spaces

TL;DR

This paper introduces a novel framework linking Hamiltonian homological vector fields to non-Abelian variational Lie algebroids, providing a new perspective on zero-curvature representations in PDEs.

Contribution

It establishes a connection between Hamiltonian homological vector fields and non-Abelian variational Lie algebroids over jet spaces, advancing the theoretical understanding of PDE symmetries.

Findings

New association between Hamiltonian homological vector fields and Lie algebroids

Framework for analyzing zero-curvature representations in PDEs

Enhanced understanding of non-Abelian variational structures

Abstract

We associate Hamiltonian homological evolutionary vector fields --which are the non-Abelian variational Lie algebroids' differentials-- with Lie algebra-valued zero-curvature representations for partial differential equations.