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In this article we prove that there exists an explicit bijection between nice -pre-Calabi–Yau algebras and -double Poisson differential graded algebras, where , 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 -double Poisson dg algebras to the partial category of -pre-Calabi–Yau algebras. Finally, we further generalize it to include double -algebras, introduced by T. Schedler.
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David Fernández, Estanislao Herscovich, Cyclic -algebras and double Poisson algebras. J. Noncommut. Geom. 15 (2021), no. 1, pp. 241–278DOI 10.4171/JNCG/412