Andre-Quillen cohomology of algebras over an operad

Details Andre-Quillen cohomology of algebras over an operad Andre-Quillen cohomology of algebras over an operad

2008-06-26

arxiv.org/abs/0806.4405v5

Adv. Math. 226 (2011), pp. 5120-5164

Mathematics

Algebraic Topology

Corrections in Sections 5 and 6, to appear in Advances in Mathematics

Scientific paper

We study the Andre-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 Andre-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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