Convergent presentations and polygraphic resolutions of associative algebras View Full Text


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Article Info

DATE

2019-03-07

AUTHORS

Yves Guiraud, Eric Hoffbeck, Philippe Malbos

ABSTRACT

Several constructive homological methods based on noncommutative Gröbner bases are known to compute free resolutions of associative algebras. In particular, these methods relate the Koszul property for an associative algebra to the existence of a quadratic Gröbner basis of its ideal of relations. In this article, using a higher-dimensional rewriting theory approach, we give several improvements of these methods. We define polygraphs for associative algebras as higher-dimensional linear rewriting systems that generalise the notion of noncommutative Gröbner bases, and allow more possibilities of termination orders than those associated to monomial orders. We introduce polygraphic resolutions of associative algebras, giving a categorical description of higher-dimensional syzygies for presentations of algebras. We show how to compute polygraphic resolutions starting from a convergent presentation, and how these resolutions can be linked with the Koszul property. More... »

PAGES

1-67

References to SciGraph publications

  • 1993. String-Rewriting Systems in NONE
  • 2006-02. Koszul and Gorenstein Properties for Homogeneous Algebras in ALGEBRAS AND REPRESENTATION THEORY
  • 2000. Gröbner Deformations of Hypergeometric Differential Equations in NONE
  • 2003. The Computer Algebra Package Bergman: Current State in COMMUTATIVE ALGEBRA, SINGULARITIES AND COMPUTER ALGEBRA
  • 1971-09. Über die deformation isolierter singularitäten analytischer mengen in INVENTIONES MATHEMATICAE
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