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Methods to Prove Koszulity of an Operad

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Algebraic Operads

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 346))

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Abstract

This chapter extends to the operadic level the various methods, obtained in Chap. 4, to prove that algebras are Koszul. They rely either on rewriting systems, PBW and Gröbner bases, distributive laws (Diamond Lemma), or combinatorics (partition poset method). The notion of shuffle operad plays a key role in this respect. We also introduce the Manin products constructions for operads.

Nous voulons, tant ce feu nous brûle le cerveau, Plonger au fond du gouffre, Enfer ou Ciel, qu’importe? Au fond de l’Inconnu pour trouver du nouveau!

Charles Baudelaire

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Authors and Affiliations

  1. IRMA, CNRS et Université de Strasbourg, Strasbourg, France

    Jean-Louis Loday

  2. Lab. de Mathématiques J.A. Dieudonné, Université de Nice-Sophia Antipolis, Nice, France

    Bruno Vallette

Authors
  1. Jean-Louis Loday
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  2. Bruno Vallette
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Loday, JL., Vallette, B. (2012). Methods to Prove Koszulity of an Operad. In: Algebraic Operads. Grundlehren der mathematischen Wissenschaften, vol 346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30362-3_8

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