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arXiv · 1902.00787

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

David Fernández·Estanislao Herscovich
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Abstract

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.

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David Fernández, Estanislao Herscovich. 2019-02-02. Cyclic $A_{\infty}$-algebras and double Poisson algebras. https://arxiv.org/abs/1902.00787

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