Cyclic $A_\infty$-algebras and double Poisson algebras - Université Grenoble Alpes
Article Dans Une Revue Journal of Noncommutative Geometry Année : 2021

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, introduced by T. Schedler.

Dates et versions

hal-04776884 , version 1 (12-11-2024)

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Citer

David Fernández, Estanislao Herscovich. Cyclic $A_\infty$-algebras and double Poisson algebras. Journal of Noncommutative Geometry, 2021, 15 (1), pp.241-278. ⟨10.4171/jncg/412⟩. ⟨hal-04776884⟩
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