# A family of the Poisson brackets compatible with the Sklyanin bracket

@article{Tsiganov2006AFO,
title={A family of the Poisson brackets compatible with the Sklyanin bracket},
author={A. V. Tsiganov},
journal={arXiv: Exactly Solvable and Integrable Systems},
year={2006}
}
• A. Tsiganov
• Published 12 December 2006
• Mathematics, Physics
• arXiv: Exactly Solvable and Integrable Systems
We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the Sklyanin bracket, and use it to derive a multi-Hamiltonian structure for a set of integrable systems that includes $XXX$ Heisenberg magnet, the open and periodic Toda lattices, the discrete self-trapping model and the Goryachev-Chaplygin gyrostat.
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