An introduction to Lie groupoids

Abstract

We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-Hölder resolutions and, subsequently, to the integration of partial differential equations. The present introduction is an extension to Lie groupoids, as far as possible, of the so well known properties and techniques much useful in Lie groups theory. We mention as far as possible since, in the case of Lie groupoids, just the first Lie Theorem holds. As for the prolongation algorithm, it is extremely useful when dealing with groupoids whereas rather senseless in the case of Lie groups.

Integration of Singular Subalgebroids

“…o o 16 Here we are applying Def. 5.3 despite the fact that R G pBq with the G-diffeology might fail to be holonomy-like.…”