Group Actions Seminar: Schillewaert, Muehlherr

The next Group Actions Seminar will be on Tuesday 6 November at the University of
Sydney.  The schedule, titles and abstracts are below.  

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11am - Noon, Carslaw 375

Speaker: Jeroen Schillewaert, The University of Auckland 
Title: On Exceptional Lie Geometries

Abstract: Parapolar spaces are point-line geometries introduced as a geometric approach 
to (exceptional) algebraic groups. We provide a characterization of a wide class of Lie 
geometries as parapolar spaces satisfying a simple intersection property. In particular 
many of the exceptional Lie geometries occur. In fact, our approach unifies and extends 
several earlier characterizations of (exceptional) Lie geometries arising from spherical 
Tits-buildings.

This is joint work with Anneleen De Schepper, Hendrik Van Maldeghem and Magali Victoor.


Noon - 2pm Lunch 

2-3pm, Carslaw 375 

Speaker: Bernhard Muehlherr, The University of Giessen
Title: Root graded groups

Abstract: A root graded group is a group containing a family of subgroups that is 
indexed by a root system and satisfies  certain commutation  relations. The  standard  
examples  are  Chevalley  groups  over  rings. The definition  of  a  root  grading  of  
a  group  is  inspired  by the corresponding  notion  for  Lie  algebras  for  which 
there are classification results due to Berman, Moody, Benkart and Zelmanov from the 
1990s.  Much less is known in the group case.

In  my  talk  I  will  address  the  classification  problem  for  root graded  groups  
and  its  connection to  the theory of buildings. It turns out that the Tits indices 
known from the classification of the semi-simple algebraic groups provide an interesting 
class of root gradings which are called stable. Any group with a stable root grading of 
rank 2 acts naturally on a bipartite graph which is called a Tits polygon. This action 
can be used to obtain classification results for groups with a stable root grading. I 
will report on several results in this direction.  These have been obtained recently in 
joint work with Richard Weiss.