SMS scnews item created by Timothy Bywaters at Tue 23 Oct 2018 1036
Type: Seminar
Distribution: World
Expiry: 6 Nov 2018
Calendar1: 6 Nov 2018 1100-1200
CalLoc1: Carslaw 375
CalTitle1: Schillewaert, On Exceptional Lie Geometries
Calendar2: 6 Nov 2018 1400-1500
CalLoc2: Carslaw 375
Auth: timothyb@dora.maths.usyd.edu.au

# 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

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.


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