Quadratic Algebras and Integrable Chains

DOI10.1093/IMRN/RNP178zbMATH Open1196.37099arXiv0811.3784OpenAlexW2025846729MaRDI QIDQ3565003

Fedor Soloviev

Publication date: 27 May 2010

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: Using Krichever-Phong's universal formula, we show that a multiplicative representation linearizes Sklyanin quadratic brackets for a multi-pole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a by-product, we obtain an extension of a Sklyanin algebra in the elliptic case. Krichever-Phong's formula provides a hierarchy of symplectic structures, and we show that there exists a non-trivial cubic bracket in Sklyanin's case.

Full work available at URL: https://arxiv.org/abs/0811.3784

zbMATH Keywords

elliptic curveLax equationSklyanin algebra

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items (1)

Master integrals, superintegrability and quadratic algebras

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