Ordering Garside groups

Diego Arcis; Luis Paris

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arXiv · 1706.00655

Ordering Garside groups

Diego Arcis·Luis Paris

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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 $\ge$ 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 $\ge$ 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

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Diego Arcis, Luis Paris. 2017-06-02. Ordering Garside groups. https://arxiv.org/abs/1706.00655

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