Curved Koszul duality theory - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematische Annalen Année : 2012

Curved Koszul duality theory

Résumé

We extend the bar-cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. We handle the lack of augmentation by extending the category of coproperads to include objects endowed with a curvature. As usual, the bar-cobar construction gives a (large) cofibrant resolution for any properad, such as the properad encoding unital and counital Frobenius algebras, a notion which appears in 2d-TQFT. We also define a curved Koszul duality theory for operads or properads presented with quadratic, linear and constant relations, which provides the possibility for smaller relations. We apply this new theory to study the homotopy theory and the cohomology theory of unital associative algebras.

Mots clés

Fichier principal
Vignette du fichier
CKD9.pdf (535.43 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00551946 , version 1 (05-01-2011)

Identifiants

Citer

Joseph Hirsh, Joan Millès. Curved Koszul duality theory. Mathematische Annalen, 2012, 354 (4), pp.1465-1520. ⟨10.1007/s00208-011-0766-9⟩. ⟨hal-00551946⟩
226 Consultations
389 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More