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.
Communicated by: R. Scharlau
Acknowledgements
The author thanks Yuni Iwamasa and Koyo Hayashi for careful reading and helpful comments, and thanks the referee for comments. The work was partially supported by JSPS KAKENHI Grant Numbers 25280004, 26330023, 26280004, 17K00029, and JST PRESTO Grant Number JPMJPR192A, Japan.
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