The Poisson bracket compatible with the classical reflection equation algebra
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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