Amphitheatre of Interdisciplinary Complex at the University of Lisbon

Iakovos Androulidakis, Instituto Superior Técnico

Geometric quantization and integrability of Lie algebroids

A classical theorem of Kostant gives the conditions for a symplectic form to be the curvature form of a Hermitian connection on a Hermitian line bundle.

We consider a generalization of this result and explain how it relates to the integrability of Lie algebroids and the classification of extensions of Lie groupoids. Also, we clarify the nature of the obstructions using the notion of a crossed module.