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arXiv · 0806.4405

André-Quillen cohomology of algebras over an operad

Joan Millès
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Abstract

We study the André-Quillen cohomology with coefficients of an algebra over an operad. Using resolutions of algebras coming from Koszul duality theory, we make this cohomology theory explicit and we give a Lie theoretic interpretation. For which operads is the associated André-Quillen cohomology equal to an Ext-functor ? We give several criterion, based on the cotangent complex, to characterize this property. We apply it to homotopy algebras, which gives a new homotopy stable property for algebras over cofibrant operads.

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BibTeXRIS

Joan Millès. 2022-10-20. André-Quillen cohomology of algebras over an operad. https://arxiv.org/abs/0806.4405

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