Ordering Garside groups

Diego Arcis (1) , Luis Paris (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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

Domaines: Théorie des groupes [math.GR]

Diego Arcis, Luis Paris. Ordering Garside groups. 2017. ⟨hal-01531275v1⟩