Double Quasi-Poisson Algebras are Pre-Calabi-Yau. (26th August 2021)

• Record Type: Journal Article
• Authors: Fernández, David; Herscovich, Estanislao
• Is Part Of: International mathematics research notices. Volume 2022:Number 23(2022)
• Page Start: 18291
• Page End: 18345
• Publication Date: 2021-08-26
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnab115
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: 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 $A_{\infty }$ -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.