13:30 → 14:20 - Abelian Tits Sets
A Tits set is a pair (G,X) consisting of a group G and a conjugacy class X of subgroups satisfying certain conditions. It is called Abelian if the elements of X are Abelian and it is called a Moufang set if any two elements of X intersect trivially.
Moufang sets were introduced by Tits in the 1990s in order to extend the Moufang property to buildings of rank one. By the classification of Moufang polygons of Tits and Weiss, each Moufang building of rank at least two is associated with a simple algebraic group over a field or a variation thereof. It is an open question whether this is also true for Moufang sets.
Examples of Tits sets can be constructed from spherical Moufang buildings by means of a Tits index. The Tits sets obtained in this fashion are called of index type. Our main result asserts that each Abelian Tits set is of index type. As a corollary, we deduce that there is a natural correspondence between indecomposable Abelian Tits sets that are not Moufang sets (up to isomorphism) and simple Jordan algebras of finite capacity that are not division algebras (up to isotopy).
This is joint work with Paulien Jansen.
Orateur : Bernhard MÜHLHERR
14:30 → 15:20 - Jacques Tits’ Work Related to the Theory of Finite (Simple) Groups
The influence of the classification of the buildings of spherical type and rank at least three on the classification of the finite simple groups and a very personal choice of some of the results of Jacques Tits on multiple transitive groups and sporadic simple groups.
Orateur : Gernot STROTH
17:00 → 17:50 - Tits-Kantor-Koecher Lie Algebras and 5 x 5-Gradings
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.
Orateur : Tom DE MEDTS
