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

2014/11/27 by Dehornoy, Patrick, Dyer, Matthew, Hohlweg, Christophe · 1 citation
#20F36 #20F55 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1411.7498

Abstract

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.

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• Garside shadows and biautomatic structures in Coxeter groups

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