Brace Bar-Cobar Duality

Using Kadeishvili's formulas with appropriate signs, we show that the classical cobar construction from coalgebras to algebras \Omega: CoAlg -> Alg can be enhanced to a functor from Hopf algebras to E_2 algebras (for a certain choice of E_2 operad) \Omega : HopfAlg -> E_2 Alg, which, unlike its classical counterpart, is not strictly adjoint, but homotopically equivalent to the left adjoint of the enhanced bar construction B: E_2 Alg -> HopfAlg studied by Gerstenhaber--Voronov and Fresse.


Publié dans:
Documenta Mathematica : Journal der deutschen Mathematiker-Vereinigung
Année
2013
ISSN:
1431-0635
Laboratoires:




 Notice créée le 2013-09-25, modifiée le 2018-12-03

Preprint:
Télécharger le document
PDF

Évaluer ce document:

Rate this document:
1
2
3
 
(Pas encore évalué)