Parabolic subgroups of Garside groups II: ribbons

Details Parabolic subgroups of Garside groups II: ribbons Parabolic subgroups of Garside groups II: ribbons

2008-11-05

arxiv.org/abs/0811.0751v1

Mathematics

Group Theory

Scientific paper

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.

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