Uniform modular lattice and Euclidean building
Hiroshi Hirai · arXiv (Cornell University) · 2017
In this paper, we present a simple lattice-theoretic characterization for Euclidean building of type A. We introduce a class of modular lattices, called uniform modular lattices, and show that uniform modular lattices and Euclidean buildings of type A constitute the same object. This is a Euclidean counterpart of the well-known equivalence between projective geometries ($\simeq$ complemented modular lattices) and spherical buildings of type A.