Infinitesimal ideal systems and the Atiyah class

Abstract

This short note gives a geometric interpretation of the Atiyah class of a Lie pair. It proves that it vanishes if the subalgebroid is the kernel of a fibration of Lie algebroids. In other words, the Atiyah class of a Lie pair vanishes if the subalgebroid is the fiber of an ideal system in the Lie algebroid. In order to prove this, a new characterisation of the ideal condition for an infinitesimal ideal system is found.