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.

中文翻译：

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统一的模块化格子和仿射建筑

摘要 获得了 A 类仿射建筑物的简单格子理论表征。我们介绍了一类模块化格子，称为统一模块化格子，并表明统一模块化格子和类型 A 的仿射建筑物构成同一对象。这是射影几何（≃ 互补模格）和 A 型球形建筑物之间众所周知的等价关系的仿射对应物。