arXiv
Open Access
2019
A characterization of simplicial oriented geometries as groupoids with root systems
Matthew Dyer
Weijia Wang
Abstrak
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 Björner-Edelman-Ziegler's lattice theoretic characterization of simplicial oriented geometries amongst oriented geometries.
Penulis (2)
M
Matthew Dyer
W
Weijia Wang
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2019
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓