Linear polygraphs and Koszulity of algebras - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2014

Linear polygraphs and Koszulity of algebras

Résumé

We define higher-dimensional linear rewriting systems, called linear polygraphs, for presentations of associative algebras, generalizing the notion of noncommutative Gröbner bases. They are constructed on the notion of category enriched in higher-dimensional vector spaces. Linear polygraphs allow more possibilities of termination orders than those associated to Gröbner bases. We introduce polygraphic resolutions of algebras giving a description obtained by rewriting of higher-dimensional syzygies for presentations of algebras. We show how to compute polygraphic resolutions starting from a convergent presentation, and how to relate these resolutions with the Koszul property of algebras.
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Dates et versions

hal-01006220 , version 1 (14-06-2014)
hal-01006220 , version 2 (21-12-2017)
hal-01006220 , version 3 (08-10-2018)

Identifiants

  • HAL Id : hal-01006220 , version 1

Citer

Yves Guiraud, Eric Hoffbeck, Philippe Malbos. Linear polygraphs and Koszulity of algebras. 2014. ⟨hal-01006220v1⟩

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