André-Quillen cohomology of algebras over an operad - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Advances in Mathematics Année : 2011

André-Quillen cohomology of algebras over an operad

Joan Millès

Résumé

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.
Fichier principal
Vignette du fichier
AQC-hal.pdf (507.32 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00551944 , version 1 (05-01-2011)
hal-00551944 , version 2 (20-10-2022)

Identifiants

Citer

Joan Millès. André-Quillen cohomology of algebras over an operad. Advances in Mathematics, 2011, 226 (6), pp.5120-5164. ⟨10.1016/j.aim.2011.01.002⟩. ⟨hal-00551944v2⟩
117 Consultations
390 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More