article
The geometry of the chamber system of a semimodular lattice
published
yes
Herbert
Abels
author 10478
10020
department
In this paper geometric properties of the following metric space C are studied. Its elements are called chambers and are the maximal chains of a semimodular lattice X of finite height and its metric d is the gallery distance. We show that X has many properties in common with buildings. More specifically, Tits [17] has recently described buildings in terms of "Weyl-group valued distance functions". We consider the Jordan-Holder permutation pi(C, D) corresponding to a pair C, D of chambers and show that it has most properties of such a distance with values in the symmetric group.
KLUWER ACADEMIC PUBL1991
eng
WEIL-GROUP VALUED DISTANCE FUNCTIONJORDAN-HOLDER PERMUTATIONSEMIMODULAR LATTICESCHUBERT SYMBOLCHAMBER SYSTEM
Order. A Journal on the Theory of Ordered Sets and its Applications
0167-8094
A1991GT4530000410.1007/BF00383400
82143-158
H. Abels, “The geometry of the chamber system of a semimodular lattice”, <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em>, vol. 8, 1991, pp. 143-158.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Abels, Herbert. 1991. “The geometry of the chamber system of a semimodular lattice”. <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em> 8 (2): 143-158.</div>
Abels H. The geometry of the chamber system of a semimodular lattice. <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em>. 1991;8(2):143-158.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Abels, H. (1991). The geometry of the chamber system of a semimodular lattice. <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em>, <em>8</em>(2), 143-158. doi:10.1007/BF00383400</div>
Abels H (1991) <br />The geometry of the chamber system of a semimodular lattice.<br />Order. A Journal on the Theory of Ordered Sets and its Applications 8(2): 143-158.
Abels, Herbert. “The geometry of the chamber system of a semimodular lattice”. <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em> 8.2 (1991): 143-158.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Abels, H. (1991). The geometry of the chamber system of a semimodular lattice. <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em>, <em>8</em>(2), 143-158. KLUWER ACADEMIC PUBL. doi:10.1007/BF00383400.</div>
Abels H (1991) <br /><em>Order. A Journal on the Theory of Ordered Sets and its Applications</em> 8(2): 143-158.
Abels, H. (1991): The geometry of the chamber system of a semimodular lattice <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em>,8:(2): 143-158.
Abels, H., 1991. The geometry of the chamber system of a semimodular lattice. <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em>, 8(2), p 143-158.
Abels, H. (1991). The geometry of the chamber system of a semimodular lattice. <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em>, <em>8</em>(2), 143-158. doi:10.1007/BF00383400
H. Abels, “The geometry of the chamber system of a semimodular lattice”, <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em>, <strong>1991</strong>, <em>8</em>, 143-158.
Abels, H.: The geometry of the chamber system of a semimodular lattice. Order. A Journal on the Theory of Ordered Sets and its Applications. 8, 143-158 (1991).
Abels, H. (1991). The geometry of the chamber system of a semimodular lattice. <em>Order. A Journal on the Theory of Ordered Sets and its Applications</em> 8, 143-158.
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