Uniform modular lattices and affine buildings
Combinatorics
2019-09-20 v2
Abstract
In this paper, we present a simple lattice-theoretic characterization for affine buildings of type A. 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.
Cite
@article{arxiv.1801.00240,
title = {Uniform modular lattices and affine buildings},
author = {Hiroshi Hirai},
journal= {arXiv preprint arXiv:1801.00240},
year = {2019}
}
Comments
ver 2; according to the suggestion of the referee, Euclidean building was changed to affine building. To appear in Advances in Geometry