Coordinates for non-integrable Lie algebroids

Abstract

We construct local coordinates for the Weinstein groupoid of a non-integrable Lie algebroid. To this end, we reformulate the notion of bi-submersion in a completely algebraic way and prove the existence of bi-submersions as such for the Weinstein groupoid. This implies that a $C^{\ast }$-algebra can be attached to every Lie algebroid.

27 pages