Journal
ANNALES HENRI POINCARE
Volume 20, Issue 8, Pages 2671-2697Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00023-019-00815-1
Keywords
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Funding
- RFBR [18-01-00926]
- Russian Academy of Sciences program Nonlinear dynamics: Fundamental Problems and Applications
- HSE University Basic Research Program
- Russian Academic Excellence Project [5-100]
- Young Russian Mathematics award
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We consider a special class of quantum nondynamical R-matrices in the fundamental representation of GLN with spectral parameter given by trigonometric solutions of the associative Yang-Baxter equation. In the simplest case N=2, these are the well-known 6-vertex R-matrix and its 7-vertex deformation. The R-matrices are used for construction of the classical relativistic integrable tops of the Euler-Arnold type. Namely, we describe the Lax pairs with spectral parameter, the inertia tensors and the Poisson structures. The latter are given by the linear Poisson-Lie brackets for the nonrelativistic models and by the classical Sklyanin-type algebras in the relativistic cases. In some particular cases, the tops are gauge equivalent to the Calogero-Moser-Sutherland or trigonometric Ruijsenaars-Schneider models.
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