Algebraic structures determined by Moufang quadranglesSpeaker: Lien Boelaert (University of Ghent)
Date: Mon 28th March 2011
Location: Mathematical Sciences Seminar Room
Moufang polygons are buildings of rank 2 that satisfy the so-called Moufang property. These geometrical structures form an alternative description of the exceptional linear algebraic groups of relative rank 2. In 2002 an entire classification of Moufang quadrangles was obtained by J. Tits and R. Weiss.
In the classification it is shown that Moufang polygons are always entirely determined by certain algebraic structures. Some examples of these are alternative division rings, cubic Jordan algebras and pseudo-quadratic spaces. The structure determining the Moufang quadrangles of type E_6, E_7 and E_8, however, is still poorly understood. We managed to associate a structurable algebra, i.e. a generalisation of algebras with involution and of Jordan algebras, to these exceptional Moufang quadrangles.
In this talk I will give an introduction to the theory of Moufang quadrangles; I will focus on how these geometrically defined objects are entirely determined by algebraic structures.
(This talk is part of the Algebra/Claude Shannon Institute series.)