Abstract
We introduce a family of compatible Poisson brackets on the space of 2 × 2 polynomial matrices, which contains the reflection equation algebra bracket. Then we use it to derive a multi-Hamiltonian structure for a set of integrable systems that includes the XXX Heisenberg magnet with boundary conditions, the generalized Toda lattices and the Kowalevski top.
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Tsiganov, A.V. The Poisson bracket compatible with the classical reflection equation algebra. Regul. Chaot. Dyn. 13, 191–203 (2008). https://doi.org/10.1134/S1560354708030052
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DOI: https://doi.org/10.1134/S1560354708030052