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Alen Đurić: Garside's coherent presentations of monoids

Date of publication: 11. 1. 2025
Algebra and functional analysis seminar
Thursday
16
January
Time:
12:30 - 13:30
Location:
FMF, Jadranska 21, predavalnica 2.03

Garside families have been introduced in order to abstract the properties which yield the greedy normal form observed in Artin-Tits monoids and in Garside monoids.

A presentation of a monoid is called coherent if it is enriched with a set of relations among relations ‘filling’ any parallel pair of sequences of relations. Deligne constructed coherent presentations for spherical Artin-Tits monoids. Gaussent, Guiraud and Malbos extended this result in two distinct directions: to all Artin-Tits monoids and to Garside monoids. In this talk, we present a unifying generalisation of these two results in the setting of Garside families.

This is a joint work with Pierre-Louis Curien and Yves Guiraud, https://hal.science/hal-03276119v4/file/coherent.pdf.