A characterization of simplicial oriented geometries as groupoids with root systems
Group Theory
2019-10-16 v1 Combinatorics
Abstract
This paper shows that simplicial oriented geometries can be characterized as groupoids with root systems having certain favorable properties, as conjectured by the first author. The proof first translates Handa's characterization of oriented matroids, as acycloids which remain acycloids under iterated elementary contractions, into the language of groupoids with root systems, then establishes favorable lattice theoretic properties of a generalization of a construction which Brink and Howlett used in their study of normalizers of parabolic subgroups of Coxeter groups and uses Bj\"orner-Edelman-Ziegler's lattice theoretic characterization of simplicial oriented geometries amongst oriented geometries.
Cite
@article{arxiv.1910.06665,
title = {A characterization of simplicial oriented geometries as groupoids with root systems},
author = {Matthew Dyer and Weijia Wang},
journal= {arXiv preprint arXiv:1910.06665},
year = {2019}
}
Comments
39 pages