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

We construct quadratic quantum algebra based on the dynamical RLL-relation for the quantum \(R\)-matrix related to \(SL(NM)\)-bundles with nontrivial characteristic class over elliptic curve. This \(R\)-matrix generalizes simultaneously the elliptic nondynamical Baxter--Belavin and the dynamical Fel...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Sechin, I A, Zotov, A V
Format: Article
Language:English
Subjects:
Algebra
Curves
Online Access:Get full text
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Summary:We construct quadratic quantum algebra based on the dynamical RLL-relation for the quantum \(R\)-matrix related to \(SL(NM)\)-bundles with nontrivial characteristic class over elliptic curve. This \(R\)-matrix generalizes simultaneously 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 particular cases \(M=1\) and \(N=1\) respectively.
ISSN:2331-8422
DOI:10.48550/arxiv.2104.04963