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Garside monoids vs divisibility monoids

2007/07/05 by Matthieu Picantin, Picantin, Matthieu
Arts and Humanities · Health Professions · #Aging, Elder Care, and Social Issues #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Health, Medicine and Society #Hermeneutics and Narrative Identity

paper · doi:10.48550/arxiv.0707.0785

openalex publication_date 2007/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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