Protoperads II: Koszul Duality

Johan Leray (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

In this paper, we construct a bar-cobar adjunction and a Koszul duality theory for protoperads, which are an operadic type notion encoding faithfully some categories of bialgebras with diagonal symmetries, like double Lie algebras (DLie). We give a criterion to show that a binary quadratic protoperad is Koszul and we apply it successfully to the protoperad DLie. As a corollary, we deduce that the properad DPois which encodes double Poisson algebras is Koszul. This allows us to describe the homotopy properties of double Poisson algebras which play a key role in non commutative geometry.

Domaines: Topologie algébrique [math.AT]

Johan Leray. Protoperads II: Koszul Duality. 2019. ⟨hal-01982392⟩