Semimodular lattices and semibuildings
type: Item
instance of: scholarly article
title: Semimodular lattices and semibuildings
zbMATH Open document ID: 0903.06007
DOI: 10.1023/A:1008667127908
author: David S. Herscovici
published in: Journal of Algebraic Combinatorics
publication date: 1999-01-05T00:00:00Z
review text: The author studies relationships between maximal chains (``flags'') in finite rank semimodular lattices. He defines a semibuilding over a Coxeter group \(W\) as a chamber system with a \(W\)-distance function and with some additional properties similar to those used by Tits to define \(W\)-buildings. He shows that finite rank semimodular lattices form an \(S_n\)-semibuilding, and develop a flag-based axiomatization of semimodular lattices. The main results consider the lattice \(L(B)\) of so-called ``\(j\)-equivalence classes'' for a semibuilding \(B\) and characterize upper semimodularity, modularity, relatively complementarity, geometricity and distributivity of \(L(B)\).
Mathematics Subject Classification ID: 06C10
zbMATH DE Number: 1139616
zbMATH Keywords: Jordan-Hölder permutation
zbMATH Keywords: maximal chains
zbMATH Keywords: finite rank semimodular lattices
zbMATH Keywords: semibuilding over a Coxeter group
zbMATH Keywords: chamber system
zbMATH Keywords: flag-based axiomatization
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
cites work: The gallery distance of flags
cites work: The geometry of the chamber system of a semimodular lattice
cites work: Q5331549
cites work: Shellable and Cohen-Macaulay Partially Ordered Sets
cites work: Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings
cites work: Q5580319
cites work: Q4693148
cites work: Q4165427
cites work: Minimal paths between maximal chains in finite rank semimodular lattices
cites work: Q3998721
cites work: Q4692803
cites work: Q3748279
cites work: Supersolvable lattices
cites work: Finite lattices and Jordan-Hölder sets
cites work: Buildings of spherical type and finite BN-pairs
cites work: Q3767490
full work available at URL: a:1008667127908
OpenAlex ID: W1776373660
description: scientific article; zbMATH DE number 1139616