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Article Dans Une Revue International Journal of Algebra and Computation Année : 2019

Ordering Garside groups

Diego Arcis
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Luis Paris
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We introduce a structure on a Garside group that we call Dehornoy structure and we show that an iteration of such a structure leads to a left-order on the group. We define two conditions on a Garside group G and we show that if G satisfies these two conditions, then G has a Dehornoy structure. Then, we show that the Artin groups of type A and of type I2(m), m≥4 satisfy these conditions, and therefore have Dehornoy structures. As indicated by the terminology, one of the orders obtained by this method on the Artin groups of type A coincides with the Dehornoy order.
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Dates et versions

hal-02194489 , version 1 (25-07-2019)



Diego Arcis, Luis Paris. Ordering Garside groups. International Journal of Algebra and Computation, 2019, 29 (05), pp.861-883. ⟨10.1142/S0218196719500322⟩. ⟨hal-02194489⟩
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