I was reading the abstract of a recent preprint (Division Algebras and Supersymmetry III by Juhn Huerta), and I wondered if something much simpler than what he was talking about had been worked on: have Lie $2$-groups been applied to the resolution of differential equations, in the same manner that Lie groups originated from the study of differential equations?

In other words, do Lie 2-groups arise as *symmetries* for (certain kinds of) differential equations, and can these in turn be used for the integration/resolution of those same differential equations? If they do not, then in what setting can a 2-group be understood as a symmetry (if any), and to what 'use' can this information be put?

My motivation here is to expand the toolset I can use to solve problems in classical analysis (like differential equations), and **not** to explore the other areas where Lie groups have developed in to (like Lie algebras and their classification, etc). For the purposes of this question, these issues are out-of-scope. In-scope are applications (to classical analysis) of generalizations going all the way to $\infty$-Lie groupoids.

symmetriesin the multivariate case. $\endgroup$ – Jacques Carette Sep 21 '11 at 18:25