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On Nahm’s equations and the Poisson structure of semi-simple complex Lie algebras. (Sur les équations de Nahm et la structure de Poisson des algèbres de Lie semi-simples complexes.) (French) Zbl 0843.53027
Using Nahm’s equations, we extend Kronheimer’s construction of hyperkähler metrics to all coadjoint orbits of a complex semisimple Lie group and more generally to symplectic leaves of holomorphic Poisson manifolds associated to the group.

MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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