JournalsjncgVol. 15, No. 1pp. 241–278

Cyclic AA_\infty-algebras and double Poisson algebras

  • David Fernández

    Universität Bielefeld, Germany
  • Estanislao Herscovich

    Université Grenoble Alpes, Gières, France
Cyclic $A_\infty$-algebras and double Poisson algebras cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

In this article we prove that there exists an explicit bijection between nice dd-pre-Calabi–Yau algebras and dd-double Poisson differential graded algebras, where dZd \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 dd-double Poisson dg algebras to the partial category of dd-pre-Calabi–Yau algebras. Finally, we further generalize it to include double PP_{\infty}-algebras, introduced by T. Schedler.

Cite this article

David Fernández, Estanislao Herscovich, Cyclic AA_\infty-algebras and double Poisson algebras. J. Noncommut. Geom. 15 (2021), no. 1, pp. 241–278

DOI 10.4171/JNCG/412