Protoperads II: Koszul Duality

Abstract : 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.
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Submitted on : Tuesday, January 15, 2019 - 4:07:46 PM
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  • HAL Id : hal-01982392, version 1
  • ARXIV : 1901.05654

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

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