André–Quillen cohomology of algebras over an operad |
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Authors: | Joan Millè s |
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Affiliation: | Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France |
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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 the 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 criteria, 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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Keywords: | André &ndash Quillen cohomology Ext-functor Operad Homotopy algebra |
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