A note on gauge systems from the point of view of Lie algebroids

TL;DR

This paper explores how irreducible gauge systems can be understood as Lie algebroids within the variational bi-complex framework, providing insights into gauge, global, and asymptotic symmetries.

Contribution

It clarifies the relationship between gauge systems and Lie algebroids, offering a unified perspective on symmetries in field theories.

Findings

Gauge systems are a specific example of Lie algebroids.

Revisits recent results on gauge and asymptotic symmetries.

Provides a geometric interpretation within the variational bi-complex.

Abstract

In the context of the variational bi-complex, we re-explain that irreducible gauge systems define a particular example of a Lie algebroid. This is used to review some recent and not so recent results on gauge, global and asymptotic symmetries.