Parabolic subgroups of Garside groups II: ribbons

Eddy Godelle (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We introduce and investigate the ribbon groupoid associated with a Garside group. Under a technical hypothesis, we prove that this category is a Garside groupoid. We decompose this groupoid into a semi-direct product of two of its parabolic subgroupoids and provide a groupoid presentation. In order to established the latter result, we describe quasi-centralizers in Garside groups. All results hold in the particular case of Artin-Tits groups of spherical type.

Domaines: Théorie des groupes [math.GR]

Eddy Godelle. Parabolic subgroups of Garside groups II: ribbons. 2008. ⟨hal-00336999⟩