Ordering Garside groups

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
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01531275
Contributeur : Luis Paris <>
Soumis le : jeudi 1 juin 2017 - 14:21:28
Dernière modification le : samedi 3 juin 2017 - 01:02:28

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  • HAL Id : hal-01531275, version 1
  • ARXIV : 1706.00655

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Diego Arcis, Luis Paris. Ordering Garside groups. 2017. <hal-01531275>

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