Page "Building (mathematics)" Paragraph 3

Iwahori – Matsumoto, Borel – Tits and Bruhat – Tits demonstrated that in analogy with Tits ' construction of spherical buildings, affine buildings can also be constructed from certain groups, namely, reductive algebraic groups over a local non-Archimedean field.

Furthermore, if the split rank of the group is at least three, it is essentially determined by its building.

Tits later reworked the foundational aspects of the theory of buildings using the notion of a chamber system, encoding the building solely in terms of adjacency properties of simplices of maximal dimension ; this leads to simplifications in both spherical and affine cases.

He proved that, in analogy with the spherical case, every building of affine type and rank at least four arises from a group.