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Pré-Publication, Document De Travail Année : 2019

Cyclic $A_{\infty}$-algebras and double Poisson algebras

David Fernández
  • Fonction : Auteur
Estanislao Herscovich

Résumé

In this article we prove that there exists an explicit bijection between nice $d$-pre-Calabi-Yau algebras and $d$-double Poisson differential graded algebras, where $d \in \mathbb{Z}$, extending a result proved by N. Iyudu and M. Kontsevich. We also show that this correspondence is functorial in a quite satisfactory way, giving rise to a (partial) functor from the category of $d$-double Poisson dg algebras to the partial category of $d$-pre-Calabi-Yau algebras. Finally, we further generalize it to include double $P_{\infty}$-algebras, as introduced by T. Schedler.

Dates et versions

hal-02009507 , version 1 (06-02-2019)

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David Fernández, Estanislao Herscovich. Cyclic $A_{\infty}$-algebras and double Poisson algebras. 2019. ⟨hal-02009507⟩

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