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Garside families in Artin-Tits monoids and low elements in Coxeter groups

We show that every finitely generated Artin-Tits group admits a finite Garside family, by introducing the notion of a low element in a Coxeter group and proving that the family of all low elements in a Coxeter system (W, S) with S finite includes S and is finite and closed under suffix and join with respect to the right weak order.

preprint2014arXivOpen access
Patrick DehornoyMatthew DyerChristophe Hohlweg
math.GR
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Open access3 authors1 topic
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Patrick DehornoyMatthew DyerChristophe Hohlweg

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