Notes on relative algebroids

TL;DR

This paper introduces relative algebroids, a unifying framework connecting Lie algebroids and partial differential equations, and explores their structural properties and applications to PDEs with symmetry.

Contribution

It provides an introductory overview of the structural theory of relative algebroids and their geometric origins, highlighting their relevance to PDEs with symmetry.

Findings

Relative algebroids unify Lie algebroids and PDEs.

They arise naturally from geometric problems.

The paper discusses their structural properties and applications.

Abstract

Relative algebroids provide a framework that unifies Lie algebroids with partial differential equations. In this set of notes, we explain how relative algebroids arise from geometric problems, and give an introduction to their structural theory. We also discuss their relation to and relevance for partial differential equations with symmetry.