Garside monoids vs divisibility monoids

Matthieu Picantin (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

Divisibility monoids (resp. Garside monoids) are a natural algebraic generalization of Mazurkiewicz trace monoids (resp. spherical Artin monoids), namely monoids in which the distributivity of the underlying lattices (resp. the existence of common multiples) is kept as an hypothesis, but the relations between the generators are not supposed to necessarily be commutations (resp. be of Coxeter type). Here, we show that the quasi-center of these monoids can be studied and described similarly, and then we exhibit the intersection between the two classes of monoids.

Mots clés: Garside monoid; divisibility monoid; quasi-center

Domaines: Théorie des groupes [math.GR]; Mathématique discrète [cs.DM]

Matthieu Picantin. Garside monoids vs divisibility monoids. 2004. ⟨hal-00160333⟩