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(Co)Homology of Algebras over 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

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.

Les mathématiques ne sont pas une moindre immensité que la mer.

Victor Hugo

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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

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  1. Jean-Louis Loday
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  2. Bruno Vallette
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Loday, JL., Vallette, B. (2012). (Co)Homology of Algebras over an Operad. In: Algebraic Operads. Grundlehren der mathematischen Wissenschaften, vol 346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30362-3_12

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