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In this article, we prove that double quasi-Poisson algebras, which are noncommutative analogues of quasi-Poisson manifolds, naturally give rise to pre-Calabi-Yau algebras. This extends one of the main results in [11], where a correspondence between certain pre-Calabi-Yau algebras and double Poisson algebras was found (see also [13, 12, 10]). However, a major difference between the pre-Calabi-Yau algebra constructed in the mentioned articles and the one constructed in this work is that the higher multiplications indexed by even integers of the underlying -algebra structure of the pre-Calabi-Yau algebra associated with double quasi-Poisson algebra do not vanish, but are given by nice cyclic expressions multiplied by explicitly determined coefficients involving the Bernoulli numbers.
Grégoire Olivier Mathys, Matthew Thomas Walters, Alexandre Mathieu Frédéric Belin