论文信息 - J ul 2 02 1 COHERENT PRESENTATIONS OF A CLASS OF MONOIDS ADMITTING A GARSIDE FAMILY

J ul 2 02 1 COHERENT PRESENTATIONS OF A CLASS OF MONOIDS ADMITTING A GARSIDE FAMILY

This paper shows how to construct coherent presentations of a class of monoids, including left-cancellative noetherian monoids containing no nontrivial invertible element and admitting a Garside family. Thereby, it resolves the question of finding a unifying generalisation of the following two distinct extensions of Deligne’s original construction of coherent presentations for spherical Artin-Tits monoids: to general Artin-Tits monoids, and to Garside monoids. The result is applied to a dual braid monoid, and to some monoids which are neither Artin-Tits nor Garside. For the Artin-Tits monoid of type Ã2, a finite coherent presentation is given, having a finite Garside family as a generating set.

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