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Pré-Publication, Document De Travail Année : 2015

Confluence algebras and acyclicity of the Koszul complex

Résumé

The N-Koszul algebras are N-homogeneous algebras which satisfy an 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 explicit our construction on several examples.
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Dates et versions

hal-01141738 , version 1 (13-04-2015)
hal-01141738 , version 2 (25-01-2016)

Identifiants

  • HAL Id : hal-01141738 , version 1

Citer

Cyrille Chenavier. Confluence algebras and acyclicity of the Koszul complex. 2015. ⟨hal-01141738v1⟩
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