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Article Dans Une Revue Algebras and Representation Theory Année : 2017

Knuth's coherent presentations of plactic monoids of type A

Nohra Hage
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Philippe Malbos

Résumé

We construct finite coherent presentations of plactic monoids of type A. Such coherent presentations express a system of generators and relations for the monoid extended in a coherent way to give a family of generators of the relations amongst the relations. Such extended presentations are used for representations of monoids, in particular, it is a way to describe actions of monoids on categories. Moreover, a coherent presentation provides the first step in the computation of a categorical cofibrant replacement of a monoid. Our construction is based on a rewriting method introduced by Squier that computes a coherent presentation from a convergent one. We compute a finite coherent presentation of a plactic monoid from its column presentation and we reduce it to a Tietze equivalent one having Knuth’s generators.
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Dates et versions

hal-01359677 , version 1 (02-09-2016)
hal-01359677 , version 2 (06-01-2018)

Identifiants

  • HAL Id : hal-01359677 , version 2

Citer

Nohra Hage, Philippe Malbos. Knuth's coherent presentations of plactic monoids of type A. Algebras and Representation Theory, 2017, 20 (5), pp.1259-1288. ⟨hal-01359677v2⟩
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