Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles

Camille Laurent-Gengoux, Friedrich Wagemann

Let K be a Lie group and P be a K-principal bundle on a manifold M. Suppose given furthermore a central extension 1\to Z\to \hat{K}\to K\to 1 of K. It is a classical question wheth…