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Funktsional'nyi Analiz i ego Prilozheniya, 2023, Volume 57, Issue 4, Pages 75–88
DOI: https://doi.org/10.4213/faa4150 (Mi faa4150) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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
Full-text PDF (640 kB) Citations (1)
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DOI: https://doi.org/10.4213/faa4150
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.
Funding agency Grant number
Russian Science Foundation 23-11-00150
Received: 29.08.2023
Revised: 29.08.2023
Accepted: 05.09.2023
English version:
Functional Analysis and Its Applications, 2023, Volume 57, Issue 4, Pages 326–336
DOI: https://doi.org/10.1134/S0016266323040068
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: G. I. Olshanski, N. A. Safonkin, “Remarks on Yangian-type algebras and double Poisson brackets”, Funktsional. Anal. i Prilozhen., 57:4 (2023), 75–88; Funct. Anal. Appl., 57:4 (2023), 326–336
Citation in format AMSBIB
\Bibitem{OlsSaf23}
\by G.~I.~Olshanski, N.~A.~Safonkin
\paper Remarks on Yangian-type algebras and double Poisson brackets
\jour Funktsional. Anal. i Prilozhen.
\yr 2023
\vol 57
\issue 4
\pages 75--88
\mathnet{http://mi.mathnet.ru/faa4150}
\crossref{https://doi.org/10.4213/faa4150}
\transl
\jour Funct. Anal. Appl.
\yr 2023
\vol 57
\issue 4
\pages 326--336
\crossref{https://doi.org/10.1134/S0016266323040068}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85178587929}
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  • https://doi.org/10.4213/faa4150
  • https://www.mathnet.ru/eng/faa/v57/i4/p75
    • This publication is cited in the following 1 articles:
    1. Grigori Olshanski, “The centralizer construction and Yangian-type algebras”, Journal of Geometry and Physics, 196 (2024), 105063  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    References:43
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