Buildings and shadows
This expository paper describes the geometries associated to simle Lie groups, following J. Tits' theory of buildings and shadows. First the definitions of ''building'', ''apartment'', ''Dynkin-diagram'' are given and motivated. Then the author describes the buildings and the associated geometries for the classical groups and for \(G_ 2\). In the last two chapters ''shadows'' are defined in order to investigate the geometries of the exceptional groups. The shadow geometry for \(E_ 8\) is explicitly derived.
scientific article; zbMATH DE number 3842131