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JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya // Archive

Funktsional. Anal. i Prilozhen., 2023 Volume 57, Issue 4, Pages 75–88 (Mi faa4150)

Remarks on Yangian-type algebras and double Poisson brackets

G. I. Olshanskiabc, N. A. Safonkinb

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b Skolkovo Institute of Science and Technology
c HSE University, Moscow

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).

Keywords: centralizer construction, Yangians, Poisson algebras, double Poisson brackets.

Received: 29.08.2023
Revised: 29.08.2023
Accepted: 05.09.2023

DOI: 10.4213/faa4150


 English version:
Functional Analysis and Its Applications, 2023, 57:4, 326–336

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© Steklov Math. Inst. of RAS, 2024