Simply laced Lie algebras with built-in structure constants
(Rutgers University & IHÉS)
Amphitéâtre Léon Motchane (IHES)
Amphitéâtre Léon Motchane
Le Bois Marie
35, route de Chartres
We construct simply laced semisimple Lie algebras L with structure constants built into the Lie bracket. This also gives structure constants for the simply connected Chevalley group associated to the Lie algebra L. For infinite dimensional simply laced Kac-Moody algebras and their associated Kac-Moody groups, we obtain a complete description of the structure constants for root vectors corresponding to real roots whose sum is real. This is joint work with Pierre Cartier.