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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 216, Number 2, Pages 203–225
DOI: https://doi.org/10.4213/tmf10488
(Mi tmf10488)
 

This article is cited in 1 scientific paper (total in 1 paper)

Higher-rank generalization of the 11-vertex rational $R$-matrix: IRF–vertex relations and the associative Yang–Baxter equation

K. R. Atalikovab, A. V. Zotovab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b National Research Centre "Kurchatov Institute", Moscow, Russia
Full-text PDF (636 kB) Citations (1)
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Abstract: We study the $\text{GL}_N$ rational $R$-matrix, which turns into the $11$-vertex $R$-matrix in the $N=2$ case. First, we describe its relations to dynamical and semidynamical $R$-matrices using the IRF–vertex type transformations. As a by-product, a new explicit form of the $\text{GL}_N$ $R$-matrix is derived. Next, we prove the quantum and the associative Yang–Baxter equations. A set of other $R$-matrix properties and $R$-matrix identities are also proved.
Keywords: rational $R$-matrix, IRF–vertex relations, associative Yang–Baxter equation.
Funding agency Grant number
Russian Science Foundation 19-11-00062
This work was supported by the Russian Science Foundation under grant No. 19-11-00062, https://rscf.ru/en/project/19-11-00062/.
Received: 04.03.2023
Revised: 04.03.2023
English version:
Theoretical and Mathematical Physics, 2023, Volume 216, Issue 2, Pages 1083–1103
DOI: https://doi.org/10.1134/S0040577923080019
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: K. R. Atalikov, A. V. Zotov, “Higher-rank generalization of the 11-vertex rational $R$-matrix: IRF–vertex relations and the associative Yang–Baxter equation”, TMF, 216:2 (2023), 203–225; Theoret. and Math. Phys., 216:2 (2023), 1083–1103
Citation in format AMSBIB
\Bibitem{AtaZot23}
\by K.~R.~Atalikov, A.~V.~Zotov
\paper Higher-rank generalization of the 11-vertex rational $R$-matrix: IRF--vertex relations and the~associative Yang--Baxter equation
\jour TMF
\yr 2023
\vol 216
\issue 2
\pages 203--225
\mathnet{http://mi.mathnet.ru/tmf10488}
\crossref{https://doi.org/10.4213/tmf10488}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4634808}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...216.1083A}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 216
\issue 2
\pages 1083--1103
\crossref{https://doi.org/10.1134/S0040577923080019}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85169151057}
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  • https://www.mathnet.ru/eng/tmf10488
  • https://doi.org/10.4213/tmf10488
  • https://www.mathnet.ru/eng/tmf/v216/i2/p203
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:31
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