# Confluence Algebras and Acyclicity of the Koszul Complex

2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : The $N$-Koszul algebras are $N$-homogeneous algebras satisfying a homological property. These algebras are characterised by their Koszul complex: an $N$-homogeneous algebra is $N$-Koszul if and only if its Koszul complex is acyclic. Methods based on computational approaches were used to prove $N$-Koszulness: an algebra admitting a side-confluent presentation is $N$-Koszul if and only if the extra-condition holds. However, in general, these methods do not provide an explicit contracting homotopy for the Koszul complex. In this article we present a way to construct such a contracting homotopy. The property of side-confluence enables us to define specific representations of confluence algebras. These representations provide a candidate for the contracting homotopy. When the extra-condition holds, it turns out that this candidate works. We make explicit our construction on several examples.
Type de document :
Article dans une revue
Algebras and Representation Theory, 2016, 〈10.1007/s10468-016-9595-6〉
Domaine :

Littérature citée [12 références]

https://hal.archives-ouvertes.fr/hal-01141738
Contributeur : Cyrille Chenavier <>
Soumis le : lundi 25 janvier 2016 - 13:54:20
Dernière modification le : jeudi 20 juillet 2017 - 09:27:05

### Fichier

Confluence algebra and acyclic...
Fichiers produits par l'(les) auteur(s)

### Citation

Cyrille Chenavier. Confluence Algebras and Acyclicity of the Koszul Complex. Algebras and Representation Theory, 2016, 〈10.1007/s10468-016-9595-6〉. 〈hal-01141738v2〉

### Métriques

Consultations de la notice

## 279

Téléchargements de fichiers