Uniform modular lattices and affine buildings
Hiroshi Hirai · Advances in Geometry · 2020
Abstract A simple lattice-theoretic characterization for affine buildings of type A is obtained. We introduce a class of modular lattices, called uniform modular lattices, and show that uniform modular lattices and affine buildings of type A constitute the same object. This is an affine counterpart of the well-known equivalence between projective geometries (≃ complemented modular lattices) and spherical buildings of type A.