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Poisson Lie groups and Hamiltonian theory of the Yang-Baxter maps

Nicolai Reshetikhin·Alexander Veselov
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Abstract

We show how the theory of Poisson Lie groups can be used to establish the Poisson properties of the Yang-Baxter maps and related transfer dynamics. As an example we present the Hamiltonian structure for the matrix KdV soliton interaction.

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Nicolai Reshetikhin, Alexander Veselov. 2005-12-29. Poisson Lie groups and Hamiltonian theory of the Yang-Baxter maps. https://arxiv.org/abs/math/0512328

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