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Abstract
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In this work, we give a method to construct compatible Poisson structures on Lie groups by means of structure constants of
their Lie algebras and some vector field. In this way we calculate some compatible Poisson structures on low-dimensional Lie
groups. Then, using a theorem by Magri and Morosi, we obtain new integrable bi-Hamiltonian systems with two-, four- and sixdimensional symplectic real Lie groups as phase spaces.
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