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TMF, 2021, Volume 208, Number 2, Pages 355–364 (Mi tmf10100)  

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

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).

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf10100

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English version:
Theoretical and Mathematical Physics, 2021, 208:2, 1156–1164

Bibliographic databases:

Received: 25.03.2021
Revised: 25.03.2021

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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