| Based on Lie-Poisson structure of Lie algebra gl(3, R), Poisson structure for semidi-rect product of Lie algebra gl(3, R) with itself is built. For the application, Gaudin model and the extension of Gaudin model are provided as illustrative examples. Under the Lie-Poisson structure, we give a Gaudin model. Futhermore, the extension of Gaudin model associated with semidirect product Lie-Poisson structure is established. Finally, Liouville integrability is proven by Lax equation. |
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