Prolongations of convenient Lie algebroids

TL;DR

This paper extends the concept of Lie algebroids to the convenient setting and explores the prolongation construction's stability under limits, broadening the theoretical framework for infinite-dimensional geometry.

Contribution

It introduces the notion of Lie algebroids in the convenient setting and adapts the prolongation construction, demonstrating its stability under projective and direct limits.

Findings

Prolongation of convenient Lie algebroids is well-defined.

Stability of prolongation under limits is established.

Framework extends finite-dimensional Lie algebroid theory to infinite dimensions.

Abstract

We first define the concept of Lie algebroid in the convenient setting. In reference to the finite dimensional context, we adapt the notion of prolongation of a Lie algebroid over a fibred manifold to a convenient Lie algebroid over a fibred manifold. Then we show that this construction is stable under projective and direct limits under adequate assumptions.