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.
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Presented by Michel Van den Bergh.
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Chenavier, C. Confluence Algebras and Acyclicity of the Koszul Complex. Algebr Represent Theor 19, 679–711 (2016). https://doi.org/10.1007/s10468-016-9595-6
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DOI: https://doi.org/10.1007/s10468-016-9595-6