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

Freeness theorems for operads via Gröbner bases
Vladimir Dotsenko
Séminaires et Congrès 26 (2013), 61-76

Résumé :
Théorèmes sur la liberté de certaines opérades par les bases de Gröbner
Nous montrons comment utiliser les bases de Gröbner des opérades pour démontrer que certaines d'entre elles sont libres : libre en tant qu'opérade non-symétrique, opérade libre comme -module pour une inclusion et opérade libre comme sous-opérade. Ceci fournit de nouvelles démonstrations pour des résultats déjà connus et permet d'en démontrer de nouveaux.

Mots-clefs : Bases de Gröbner, théorèmes libres.

Abstract:
We show how to use Gröbner bases for operads to prove various freeness theorems: freeness of certain operads as nonsymmetric operads, freeness of an operad as a -module for an inclusion , freeness of a suboperad. This gives new proofs of many known results of this type and helps to prove some new results.

Keywords: Gröbner bases, shuffle operads, freeness theorems.

Class. math. : Primary: 18D50; Secondary: 08B20, 16S15.

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

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