(Co)Homology of Algebras over an Operad

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

Abstract

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.

Keywords

Algebra Structure Vertex Operator Algebra Abelian Extension Cochain Complex Infinitesimal Deformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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