Type: Seminar

Distribution: World

Expiry: 6 Nov 2018

CalTitle1: Schillewaert, On Exceptional Lie Geometries

Calendar2: 6 Nov 2018 1400-1500

CalLoc2: Carslaw 375

CalTitle2: Muehlherr, Root graded groups

Auth: timothyb@dora.maths.usyd.edu.au

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

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