(Co)Homology of Algebras over an Operad

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


In this chapter, we introduce the André–Quillen cohomology and homology for algebras over an operad, which provides us with homological invariants. It plays a role in many classification problems, like for instance deformation theory. We use the resolutions provided by the Koszul duality theory to make explicit small chain complexes which computes it.


Algebra Structure Vertex Operator Algebra Abelian Extension Cochain Complex Infinitesimal Deformation 
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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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