Crossed modules of Lie algebras and 2-r-matrices

Cirio-Martins (Advances 2015) categorify r-matrices and infinitesimal braidings in order to strive for a categorification of Vassiliev knot invariants. The place of a Lie algebra in their setting is taken by a crossed module of Lie algebras, as the easiest version of a Lie 2-algebra. Their main example is the "string Lie algebra", i.e. a crossed module constructed in 2006 by me which represents the non trivial class in $H^3(g)$ for the simple Lie algebra $g=sl_2(\mathbb{C})$. In our work with Salim Rivière (Angers), we extend Cirio-Martin's work to all simple Lie algebra and beyond.