Abstract
In a recent paper, one of the authors proposed a construction of associative algebras which share a number of properties of the Yangians of series A but are more massive. We show that this construction admits a generalization which reveals a direct connection with a large family of double Poisson brackets on free associative algebras, which was described by Pichereau and Van de Weyer (in 2008).
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References
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Funding
This research was supported by the Russian Science Foundation under project 23-11-00150.
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2023, Vol. 57, pp. 75–88 https://doi.org/10.4213/faa4150.
To the 110th birthday of Israel Moiseevich Gel’fand
Translated by G. I. Olshanski and N. A. Safonkin
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Olshanski, G.I., Safonkin, N.A. Remarks on Yangian-Type Algebras and Double Poisson Brackets. Funct Anal Its Appl 57, 326–336 (2023). https://doi.org/10.1134/S0016266323040068
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DOI: https://doi.org/10.1134/S0016266323040068