Garside families in Artin-Tits monoids and low elements in Coxeter groups
Group Theory
2014-12-01 v1
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.
Keywords
Cite
@article{arxiv.1411.7498,
title = {Garside families in Artin-Tits monoids and low elements in Coxeter groups},
author = {Patrick Dehornoy and Matthew Dyer and Christophe Hohlweg},
journal= {arXiv preprint arXiv:1411.7498},
year = {2014}
}