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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 208, Number 2, Pages 355–364
DOI: https://doi.org/10.4213/tmf10100 (Mi tmf10100) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Quadratic algebras based on $SL(NM)$ elliptic quantum $R$-matrices

I. A. Sechinab, A. V. Zotovac

a National Research University "Higher School of Economics", Moscow, Russia
b Center for Advanced Studies, Skolkovo Institute of Science and Technology, Moscow, Russia
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf10100
Abstract: We construct a quadratic quantum algebra based on the dynamical $RLL$-relation for the quantum $R$-matrix related to $SL(NM)$-bundles with a nontrivial characteristic class over an elliptic curve. This $R$-matrix simultaneously generalizes the elliptic nondynamical Baxter–Belavin and the dynamical Felder $R$-matrices, and the obtained quadratic relations generalize both the Sklyanin algebra and the relations in the Felder–Tarasov–Varchenko elliptic quantum group, which are reproduced in the respective particular cases $M=1$ and $N=1$.
Keywords: quantum quadratic algebras, elliptic integrable system, quantum dynamical $R$-matrix.
Funding agency Grant number
Russian Science Foundation 21-41-09011
This research is supported by a grant from the Russian Science Foundation (Project No. 21-41-09011).
Received: 25.03.2021
Revised: 25.03.2021
English version:
Theoretical and Mathematical Physics, 2021, Volume 208, Issue 2, Pages 1156–1164
DOI: https://doi.org/10.1134/S0040577921080110
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. A. Sechin, A. V. Zotov, “Quadratic algebras based on $SL(NM)$ elliptic quantum $R$-matrices”, TMF, 208:2 (2021), 355–364; Theoret. and Math. Phys., 208:2 (2021), 1156–1164
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
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