Ordering Garside groups
Group Theory
2018-06-11 v2
Abstract
We introduce a condition on Garside groups that we call Dehornoy structure. An iteration of such a structure leads to a left order on the group. We show conditions for a Garside group to admit a Dehornoy structure, and we apply these criteria to prove that the Artin groups of type A and I 2 (m), m 4, have Dehornoy structures. We show that the left orders on the Artin groups of type A obtained from their Dehornoy structures are the Dehornoy orders. In the case of the Artin groups of type I 2 (m), m 4, we show that the left orders derived from their Dehornoy structures coincide with the orders obtained from embeddings of the groups into braid groups. 20F36
Cite
@article{arxiv.1706.00655,
title = {Ordering Garside groups},
author = {Diego Arcis and Luis Paris},
journal= {arXiv preprint arXiv:1706.00655},
year = {2018}
}