Rewriting systems in sufficiently large Artin-Tits groups

JOURNAL OF ALGEBRA

卷:466

Article

Godelle, Eddy^1,2,3  Rees, Sarah⁴ 

[1] Normandie Univ, Caen, France

[2] UNICAEN, LMNO, F-14032 Caen, France

[3] CNRS, UMR 6139, F-14032 Caen, France

[4] Newcastle Univ, Sch Math & Stat, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

关键词: Artin-Tits groups;    Large type;    Word problem;   

DOI  :  10.1016/j.jalgebra.2016.07.031

来源: Elsevier

【 摘 要 】

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 word using 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 free reduction, but without introducing trivial factors ss(-1) or s(-1) s. This conjecture is 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free