On ideals in Lie algebroids

I will describe a notion of ideals in Lie algebroids, named 'infinitesimal ideal systems' and motivate from several point of views why this is in my opinion the 'right' notion of symmetry in the Lie algebroid setting: I will discuss quotients by infinitesimal ideal systems, their equivalence to multiplicative foliations on Lie groupoids, and how they define sub-representations of Lie algebroids adjoint representations (up to homotopy). ' Then I will define the Atiyah class of an infinitesimal ideal system, and describe a first obstruction to the existence of an infinitesimal ideal system structure on a Lie pair.

This is partly based on joint work with Drummond and Ortiz.