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Hamiltonian dynamics on matched pairs
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Hamiltonian dynamics on matched pairs
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It is shown that the cotangent bundle of a matched pair Lie group is itself a matched pair Lie group. The trivialization of the cotangent bundle of a matched pair Lie group are presented. On the trivialized space, the canonical symplectic two-form and canonical Poisson bracket are explicitly written. Various symplectic and Poisson reductions are perfomed. The Lie-Poisson bracket is derived. As an example, Lie-Poisson equations on $\mathfrak{sl}(2,\mathbb{C})^\ast$ are obtained.
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