Airy Structures for Semisimple Lie Algebras

Abstract We give a complete classification of Airy structures for finite-dimensional simple Lie algebras over $${\mathbb {C}}$$ C , and to some extent also {R}}$$ R up isomorphisms gauge transformations. The result is that the only this type which admit any are $$\mathfrak {sl}_2$$ sl 2 {sp}_4$$ sp 4 {sp}_{10}$$ 10 . Among these, each admits exactly two non-equivalent structures. Our methods apply directly semisimple algebras. In case it turns out number countably infinite. have derived interesting properties these constructed many examples. Techniques used derive our results may be described, broadly speaking, as an application representation theory in semiclassical analysis.