Uniform modular lattices and affine buildings

被引：7
作者：
Hirai, Hiroshi [1 ]
机构：
[1] Univ Tokyo, Grad Sch Informat Sci & Technol, Dept Math Informat, Tokyo 1138656, Japan
来源：
ADVANCES IN GEOMETRY | 2020年 / 20卷 / 03期
关键词：
Modular lattice; affine building of type A;
D O I：
10.1515/advgeom-2020-0007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 (similar or equal to complemented modular lattices) and spherical buildings of type A.
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收藏
页码：375 / 390
页数：16
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