Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms

TL;DR

This paper introduces higher algebroids as a generalization of Lie algebroids using vector bundle comorphisms, expanding the framework for geometric structures in mechanics.

Contribution

It presents a novel definition of higher algebroids based on graded-linear bundle comorphisms, extending the classical Lie algebroid concept.

Findings

Defined higher algebroids via vector bundle comorphisms

Provided natural examples of higher algebroids

Discussed applications in geometric mechanics

Abstract

We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a special kind. In our approach higher algebroids are vector bundle comorphism between graded-linear bundles satisfying natural axioms. We provide natural examples and discuss applications in geometric mechanics.