Euclidean buildings

Guy Rousseau (1)

1 IECN - Institut Élie Cartan de Nancy

We give a general presentation of euclidean buildings. This includes vectorial buildings (a variety of Tits buildings) and affine buildings (e.g. Bruhat-Tits buildings. For the general definition the emphasis is given to facets (even in the non-discrete case). More details are given for the buildings of the reductive group GL(n).

Mots clés: building; apartment; reductive group; Bruhat-Tits

Domaines: Théorie des groupes [math.GR]

Guy Rousseau. Euclidean buildings. Géométries à courbure négative ou nulle, groupes discrets et rigidité, Jun 2004, Grenoble, France. pp.77-116. ⟨hal-00094363⟩