John led the discussion last week. I am a bit late in posting as I have been busy organising the WA Junior Olympiad which was on Saturday.

The topic this week is what is called *Buekenhout geometries *or *diagram geometries*. We also have a new name.

As we have seen so far, a projective space can be associated with the Dynkin diagram of type and polar spaces can be associated with the Dynkin diagram of type . Tits’ theory of buildings generalises these notions and associates to each simple group of Lie type a geometry known as a building and this building can be encoded in the Dynkin diagram associated with the group. In his seminal 1979 paper, `Diagrams for geometries and groups’ in JCTA, Francis Buekenhout looked to generalise this further and introduced the notion of diagram geometries. These are also referred to as Buekenhout geometries.

Continue reading “Buildings, Geometries and Algebraic Groups Study Group IV”