Banach Lie algebroids

TL;DR

This paper extends the concept of second order differential equations to anchored Banach vector bundles and introduces Banach Lie algebroids, establishing their categorical structure.

Contribution

It generalizes Lie algebroids to infinite-dimensional Banach bundles and proves their categorical properties.

Findings

Banach Lie algebroids are well-defined structures.

The category of Banach Lie algebroids is established.

Extension of SODEs to Banach vector bundles.

Abstract

First, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.