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- W774334676 abstract "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." @default.
- W774334676 created "2016-06-24" @default.
- W774334676 creator A5016694492 @default.
- W774334676 date "2015-04-13" @default.
- W774334676 modified "2023-09-25" @default.
- W774334676 title "Confluence algebras and acyclicity of the Koszul complex" @default.
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- W774334676 hasPublicationYear "2015" @default.
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