Alternating normal forms for braids and locally Garside monoids

Patrick Dehornoy (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We describe new types of normal forms for braid monoids, Artin-Tits monoids, and, more generally, all monoids in which divisibility has some convenient lattice properties ("locally Garside monoids"). We show that, in the case of braids, one of these normal forms turns out to coincide with the normal form introduced by Burckel and deduce that the latter can be computed easily. This approach leads to a new, simple description for the canonical well-order of Bn+ in terms of that of B(n-1)+.

Mots clés: braid ordering; tree; Garside monoid; Artin--Tits monoid; locally Garside monoid; braid group

Domaines: Théorie des groupes [math.GR]

Patrick Dehornoy. Alternating normal forms for braids and locally Garside monoids. 2007. ⟨hal-00132277v2⟩