Separation of Variables, Quasi-Trigonometric 𝑟-Matrices and Generalized Gaudin Models

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2021
• 1. Verfasser: Skrypnyk, Taras
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2021
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/211354
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Separation of Variables, Quasi-Trigonometric 𝑟-Matrices and Generalized Gaudin Models. Taras Skrypnyk. SIGMA 17 (2021), 069, 21 pages

We construct two new one-parametric families of separated variables for the classical Lax-integrable Hamiltonian systems governed by a one-parametric family of non-skew-symmetric, non-dynamical 𝖌𝔩(2)⊗𝖌𝔩(2)-valued quasi-trigonometric classical 𝑟-matrices. We show that for all but one classical 𝑟-matr...