Although every finite dimensional Lie algebra integrates to a global Lie group, it is well known that this does not hold for Lie algebroids (or for infinite dimensional Lie algebras), which may fail to integrate to global objects. On the other hand, every Lie algebra(oid) integrates to a local Lie group(oid). This talk aims at explaining how to conciliate these two different perspectives, from which a somewhat unexpected relationship between the failure in integrability and the lack of associativity will emerge.

This talk is based on joint work with Daan Michiels.