Algorithms for Garside calculus

Patrick Dehornoy (1) , Volker Gebhardt (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 SCEM - School of Computing, Engineering and Mathematics [Sydney]

Garside calculus is the common mechanism that underlies a certain type of normal form for the elements of a monoid, a group, or a category. Originating from Garside's approach to Artin's braid groups, it has been extended to more and more general contexts, the latest one being that of categories and what are called Garside families. One of the benefits of this theory is to lead to algorithms solving effectively the naturally occurring problems, typically the Word Problem. The aim of this paper is to present and solve these algorithmic questions in the new extended framework.

Mots clés: normal form; word problem; category presentation; groupoid of fractions; Garside calculus; Garside family; germ

Domaines: Théorie des groupes [math.GR]

Patrick Dehornoy, Volker Gebhardt. Algorithms for Garside calculus. 2013. ⟨hal-00776088⟩