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Double Quasi-Poisson Algebras are Pre-Calabi-Yau

Publicado en:International Mathematics Research Notices. 2022 (23): 18291-18345 - 2022-01-01 2022(23), DOI: 10.1093/imrn/rnab115

Autores: Fernández D; Herscovich E

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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 A∞-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. © The Author(s) 2021. Published by Oxford University Press. All rights reserved.

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