November 3, 2014
Arturo Pianzola, University of Alberta

What is an affine Kac-Moody Lie algebra? (D'apres Demazure-Grothendieck; circa 1963)

This talk is intended for a general audience. No knowledge of infinite dimensional Lie theory is needed, and the affine algebras are an "excuse" to discuss, mostly by concrete examples, a bridge between infinite dimensional Lie theory and SGA3. The title of this talk is (intentionally) misleading: Kac-Moody Lie algebras did not exist in 1963. That said, over the last decade substantial results on infinite dimensional Lie theory have been proven using the theory of reductive group schemes [SGA3] developed by Demazure and Grothendieck. One can therefore ask, a posteriori, what are the affine algebras in the language of [SGA3]. It is an intriguing question with an elegant answer that naturally leads to a (new) family of infinite dimensional Lie algebras related to Grothendieck's dessins d'enfants.