[Présentations pour les monoı̈des de tresses duaux]
Birman, Ko et Lee ont introduit un nouveau monoı̈ de —avec une présentation explicite—dont le groupe de fractions est le groupe des tresses à n brins. Suivant une nouvelle approche proposée avec Digne et Michel, Bessis a défini un monoı̈ de de tresses dual pour tout groupe d'Artin–Tits de type de Coxeter fini généralisant le cas du type A. Ici, nous donnons une présentation explicite de ce monoı̈de de tresses dual pour les groupes d'Artin–Tits de type B et D, et nous étudions la combinatoire des structures de Garside sous-jacentes.
Birman, Ko and Lee have introduced a new monoid —with an explicit presentation—whose group of fractions is the n-strand braid group . Building on a new approach by Digne, Michel and himself, Bessis has defined a dual braid monoid for every finite Coxeter type Artin–Tits group extending the type A case. Here, we give an explicit presentation for this dual braid monoid in the case of types B and D, and we study the combinatorics of the underlying Garside structures.
@article{CRMATH_2002__334_10_843_0,
author = {Picantin, Matthieu},
title = {Explicit presentations for the dual braid monoids},
journal = {Comptes Rendus. Math\'ematique},
pages = {843--848},
publisher = {Elsevier},
volume = {334},
number = {10},
year = {2002},
doi = {10.1016/S1631-073X(02)02370-1},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02370-1/}
}
TY - JOUR AU - Picantin, Matthieu TI - Explicit presentations for the dual braid monoids JO - Comptes Rendus. Mathématique PY - 2002 SP - 843 EP - 848 VL - 334 IS - 10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02370-1/ DO - 10.1016/S1631-073X(02)02370-1 LA - en ID - CRMATH_2002__334_10_843_0 ER -
%0 Journal Article %A Picantin, Matthieu %T Explicit presentations for the dual braid monoids %J Comptes Rendus. Mathématique %D 2002 %P 843-848 %V 334 %N 10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02370-1/ %R 10.1016/S1631-073X(02)02370-1 %G en %F CRMATH_2002__334_10_843_0
Picantin, Matthieu. Explicit presentations for the dual braid monoids. Comptes Rendus. Mathématique, Tome 334 (2002) no. 10, pp. 843-848. doi : 10.1016/S1631-073X(02)02370-1. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02370-1/
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