Variational Lie algebroids and homological evolutionary vector fields

TL;DR

This paper introduces a novel framework for Lie algebroids over infinite jet spaces, establishing their equivalence with homological evolutionary vector fields, which advances the mathematical understanding of these structures.

Contribution

It provides a new definition of Lie algebroids over infinite jet spaces and demonstrates their equivalence with homological evolutionary vector fields, bridging two mathematical concepts.

Findings

Defined Lie algebroids over infinite jet spaces

Established equivalence with homological evolutionary vector fields

Enhanced understanding of geometric structures in differential geometry

Abstract

We define Lie algebroids over infinite jet spaces and establish their equivalent representation through homological evolutionary vector fields.