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
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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