On the integration of transitive Lie algebroids

Abstract

We revisit the problem of integrating Lie algebroids A ⇒ M to Lie groupoids G ⇒ M , for the special case that the Lie algebroid A is transitive. We obtain a geometric explanation of the Crainic-Fernandes obstructions for this situation, and an explicit construction of the integration whenever these obstructions vanish. We also indicate an extension of this approach to regular Lie algebroids.