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February 6-10, 2012
Ghent (Belgium)

Organizers:

Bart De Bruyn,
Tom De Medts,
Jef Thas,
Koen Thas,
Hendrik Van Maldeghem

 


Arjeh Cohen

Root group geometries, Lie algebras, and polar spaces

The shadow geometries of spherical buildings corresponding to root nodes have been characterized as point-line incidence systems in terms of what is called root filtration spaces. This characterization is useful in that abstract root groups as introduced by Timmesfeld and simple Lie algebras over a field char. at least 5 containing an extremal element are easily seen to lead to root filtrations spaces. I will survey these developments and focus on two questions of more recent research:

  1. To what extent is the above Lie algebra structure determined by the root filtration space?
  2. Is there a direct proof of the characterization as a root filtration space of the line Grassmannians of polar spaces?