HYPER-LIE POISSON STRUCTURES

The main purpose of the paper is to study hyperkahler structures from the viewpoint of symplectic geometry. We introduce a notion of hypersy mplectic structures which encompasses that of hyperkahler structures. Motivated by the work of Kronheimer on (co)adjoint orbits of semi-simp le Lie algebras [10], [11], we define hyper-lie Poisson structures ass ociated with a compact semi-simple Lie algebra and give criterion whic h implies their existence. We study an explicit example of a hyper-lie Poisson structure, in which the moduli spaces of solutions to Nahm's equations assocaited to Lie algebra su(2) are realized as hypersymplec tic leaves and are related to the (co)adjoint orbits of sl(2, C).