Methods to Prove Koszulity of an Operad

  • Jean-Louis Loday
  • Bruno Vallette
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 346)


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.


Maximal Chain White Product Black Product Symmetric Monoidal Category Koszul Duality 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jean-Louis Loday
    • 1
  • Bruno Vallette
    • 2
  1. 1.IRMA, CNRS et Université de StrasbourgStrasbourgFrance
  2. 2.Lab. de Mathématiques J.A. DieudonnéUniversité de Nice-Sophia AntipolisNiceFrance

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