Orateur
Tom DE MEDTS
Description
The classical Tits-Kantor-Koecher construction produces a Lie algebra starting from a Jordan algebra; the resulting Lie algebra is 3-graded. This can be generalized to other algebraic structures as input, giving rise to 5-graded Lie algebras.
From a completely different point of view, Tits and Weiss have developed algebraic structures that parametrize spherical buildings associated with isotropic simple linear algebraic groups; the most complicated of those are the “quadrangular algebras” introduced by Weiss.
We combine both ideas, and we show that Lie algebras equipped with two different 5-gradings give rise, under some natural conditions, to quadrangular algebras.
This is based on joint work with Jeroen Meulewaeter.
