In a recent paper Ballersteros and Ragnisco (1998) have proposed a new method of constructing integrable Hamiltonian systems. A new class of integrable systems may be devised using the following sequence: \documentclass[12pt]{minimal}
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$$\mathcal{A} \to \Lambda \to C \to \tilde \Lambda \to \{ .,\;.\} _{\tilde \Lambda } \to (A,\;\vartriangle )$$
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$${\text{(R}}^{\text{3}} ,[.,\;.]),\;\Lambda $$
\end{document} is a Lie–Poisson structure on R3, C is a Casimir for \documentclass[12pt]{minimal}
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$$\Lambda ,\;\{ .,\;.\} _{\tilde \Lambda } $$
\end{document} is a reduced Poisson bracket and (A, ▵) is a bialgebra. We study the relation between a Lie-Poisson stucture Λ and a reduced Poisson bracket \documentclass[12pt]{minimal}
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$$\{ ,\;\} _{\tilde \Lambda } $$
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