Double Quasi-Poisson Algebras are Pre-Calabi-Yau
Publicated to:International Mathematics Research Notices. 2022 (23): 18291-18345 - 2022-01-01 2022(23), DOI: 10.1093/imrn/rnab115
Authors: Fernández D; Herscovich E
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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∞-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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The work has been published in the journal International Mathematics Research Notices due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2022, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics (Miscellaneous). Notably, the journal is positioned above the 90th percentile.
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Leadership analysis of institutional authors
This work has been carried out with international collaboration, specifically with researchers from: France; Germany.
There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (FERNANDEZ ALVAREZ, DAVID) .