Since Baumslag and Roseblade discovered that finitely presented subgroups of a product of two free groups must be virtually a product of free groups there has been an intensive research on properties of subdirect products of groups mainly focusing on the homological and homotopical properties, including the celebrated 1-2-3 Theorem by Bridson, Howier, Miller and Short. In this talk we will discuss how to extend some of these results to Lie algebras.

This is a joint work with Dessislava Kochloukova