PreprintCC BY 4.0arXiv
Ordering, Artin--Tits group, Garside structure
Abstract
A Dehornoy structure is a tool used to obtain a left order in the Garside group~G. Arcis and Paris introduced two conditions, known as Condition~A and Condition~B. When they are both satisfied, they ensure that~G possesses a Dehornoy structure. These two conditions describes how the product in the corresponding monoid behaves with an alternating decomposition. Here, we consider the case of a spherical type Artin group~G. We prove that Condition A almost always holds, but Condition~B is rarely satisfied.
Related
- Alternating decomposition of a product in a spherical type Artin-Tits monoid
- Quasipositive Braids, Presentations, and Garside Structures
- The dual of the Tits cone and dominance of Coxeter groups
- Representation Type and Schurian Finiteness of Tits Algebras
- The Lie algebra structure of HH1(B) for blocks with a normal defect group
BibTeX
@misc{fromentin2026ordering,
title = {{Ordering, Artin--Tits group, Garside structure}},
author = {Jean Fromentin and Eddy Godelle},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04757},
eprint = {2609.04757},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04757},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ordering, Artin--Tits group, Garside structure
AU - Jean Fromentin
AU - Eddy Godelle
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04757
UR - https://arxiv.org/abs/2609.04757
AB - A Dehornoy structure is a tool used to obtain a left order in the Garside group~G. Arcis and Paris introduced two conditions, known as Condition~A and Condition~B. When they are both satisfied, they ensure that~G possesses a Dehornoy structure. These two conditions describes how the product in the corresponding monoid behaves with an alternating decomposition. Here, we consider the case of a spherical type Artin group~G. We prove that Condition A almost always holds, but Condition~B is rarely satisfied.
ER -