Confluence of linear rewriting and homology of algebras

Yves Guiraud (1, 2) , Eric Hoffbeck (3) , Philippe Malbos (2, 4)

1 PPS - Preuves, Programmes et Systèmes
2 PI.R2 - Design, study and implementation of languages for proofs and programs
3 LAGA - Laboratoire Analyse, Géométrie et Applications
4 AGL - Algèbre, géométrie, logique

We introduce the notion of higher dimensional linear rewriting systems for presentations of algebras, generalizing the notion of non-commutative Gröbner bases. We show how to use this notion to compute homological invariants of associative algebras, using the confluence properties of presentations of these algebras. Our method constitutes a new application of confluence in algebra.

Domaines: Catégories et ensembles [math.CT]; K-théorie et homologie [math.KT]

Yves Guiraud, Eric Hoffbeck, Philippe Malbos. Confluence of linear rewriting and homology of algebras. 3rd International Workshop on Confluence, Jul 2014, Vienna, Austria. ⟨hal-01105087⟩