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arXiv · 1801.00240

Uniform modular lattices and affine buildings

Hiroshi Hirai
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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 ($\simeq$ complemented modular lattices) and spherical buildings of type A.

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Hiroshi Hirai. 2019-09-18. Uniform modular lattices and affine buildings. https://arxiv.org/abs/1801.00240

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