SMF - Publications - Séminaires et Congrès - Titles

Operads 2009
VERSION IMPRIMEE A VENIR - PRINT VERSION NOT YET AVAILABLE
Loday, Jean-Louis and Vallette, Bruno, eds
Séminaires et Congrès 26 (2013), 281 pages
Presentation, Summary

Diagram rewriting and operads
Yves Lafont
Séminaires et Congrès 26 (2013), 163-179

Résumé :
Réécriture de diagrammes et opérades
Nous donnons un aperçu de la syntaxe diagrammatique pour les PROs et les PROPs, qui sont liés à la théorie des opérades et des bigèbres. En utilisant la réécriture de diagrammes, on obtient des présentations de PROs par générateurs et relations. Dans certains cas, on obtient même des systèmes de réécriture convergents.

Mots-clefs : Complétion de Knuth-Bendix, confluence, enchevÍtrement, foncteur de Schur, forme canonique, opérade, présentation par générateurs et relations, PRO, PROP, réécriture de diagrammes, théorie algébrique, tresse.

Abstract:
We give a survey of a diagrammatic syntax for PROs and PROPs, which are related to the theory of operads and bialgebras. Using diagram rewriting, we obtain presentations of PROs by generators and relations. In some cases, we even get convergent rewrite systems.

Keywords: Algebraic theory, braid, canonical form, confluence, diagram rewriting, Knuth-Bendix completion, operad, permutation, presentation by generators and relations, PRO, PROP, Schur functor, tangle.

Class. math. : 18C10.

ISBN : 978-2-85629-363-8
ISSN : 1285-2783

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