Lie ideals play a central role in the representation and classification theory of Lie algebras. In this talk, we will explore their deformation theory by introducing the differential graded Lie algebra that governs their deformation problem and by relating it to other well-known deformation theories. We will also discuss geometric applications of this framework, including results on rigidity, stability, and obstructions to infinitesimal deformations.
This is based on joint work with Madeleine Jotz.