The well-ordering of dual braid monoids

Jean Fromentin (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We describe the restriction of the Dehornoy ordering of braids to the dual braid monoids introduced by Birman, Ko and Lee: we give an inductive characterization of the ordering of the dual braid monoids and compute the corresponding ordinal type. The proof consists in introducing a new ordering on the dual braid monoid using the rotating normal form of arXiv:math.GR/0811.3902, and then proving that this new ordering coincides with the standard ordering of braids.

Mots clés: braid; order type; ordering; well-ordering; normal form; dual braid monoid; rotating normal form

Domaines: Théorie des groupes [math.GR]

Jean Fromentin. The well-ordering of dual braid monoids. 2007. ⟨hal-00200732v2⟩