School of Mathematical Sciences

Fischer spaces and Lie algebras menu

Fischer spaces and Lie algebras

Hans Cuypers (Eindhoven)
Mon, 16/11/2009 - 16:30
Seminar series: 

A Fischer space is a partial linear space (P,L) in which
each line contains 3 points and two intersecting lines
generate a subspace isomorphic to an affine or dual affine plane.

Starting from a Fischer space (P,L) one can construct an
algebra on the vector space 2^P defined by the rule that

p*q=p+q+r if {p,q,r} is a line
                   =0     if p and q are not collinear or p=q.

We study the structure of this algebra and determine the
simple Lie algebras that arise from this construction.