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arXiv · 2002.10495

Double quasi-Poisson algebras are pre-Calabi-Yau

David Fernández·Estanislao Herscovich
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Abstract

In this article we prove that double quasi-Poisson algebras, which are non-commutative analogues of quasi-Poisson manifolds, naturally give rise to pre-Calabi-Yau algebras. This extends one of the main results in [11] (see also [10]), where a relationship between pre-Calabi-Yau algebras and double Poisson algebras was found. 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 $A_{\infty}$-algebra structure of the pre-Calabi-Yau algebra associated to a double quasi-Poisson algebra do not vanish, but are given by nice cyclic expressions multiplied by explicitly determined coefficients involving the Bernoulli numbers.

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David Fernández, Estanislao Herscovich. 2020-02-24. Double quasi-Poisson algebras are pre-Calabi-Yau. https://arxiv.org/abs/2002.10495

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