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Rewriting systems in sufficiently large Artin-Tits groups

Lookup NU author(s): Professor Sarah Rees

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Abstract

A conjecture of Dehornoy claims that, given a presentation of an Artin-Tits group, every word that represents the identity can be transformed into the trivial wordusing the braid relations, together with certain rules(between pairs of words that are not both positive)that can be derived directly from the braid relations, as well as freereduction, but without introducing trivial factors $ss^{-1} $ or $s^{-1} s$. This conjectureis known to be true for Artin-Tits groups of spherical type or of FC type. We prove the conjecture for Artin--Tits groups of sufficiently large type.

Publication metadata

Author(s): Godelle E, Rees S

Publication type: Article

Publication status: Published

Journal: Journal of Algebra

Year: 2016

Volume: 466

Pages: 284-307

Print publication date: 15/11/2016

Online publication date: 09/08/2016

Acceptance date: 24/06/2016

Date deposited: 15/09/2016

ISSN (print): 0021-8693

ISSN (electronic): 1090-266X

Publisher: Elsevier

URL: http://dx.doi.org/10.1016/j.jalgebra.2016.07.031

DOI: 10.1016/j.jalgebra.2016.07.031

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