Interior and Exterior Differential Systems for Lie Algebroids

TL;DR

This paper extends classical differential system theories to Lie algebroids, presenting Maurer-Cartan and Cartan type theorems for interior and exterior differential systems within this generalized framework.

Contribution

It introduces the notions of interior and exterior differential systems for Lie algebroids and proves corresponding Cartan type theorems, expanding the classical theory to a broader setting.

Findings

Maurer-Cartan type theorem for Lie algebroids

Cartan type theorem for interior differential systems

Extension of exterior differential systems to Lie algebroids

Abstract

A theorem of Maurer-Cartan type for Lie algebroids is presented. Suppose that any vector subbundle of a Lie algebroid is called interior differential system (IDS) for that Lie algebroid. A theorem of Cartan type is obtained. Extending the classical notion of exterior differential system (EDS) to Lie algebroids, a theorem of Cartan type is obtained.