1996/05/19 by Ping Xu, Xu, Ping
Earth and Planetary Sciences · Environmental Science · Materials Science · Mathematics · #Geological Modeling and Analysis #Methane Hydrates and Related Phenomena #Silicone and Siloxane Chemistry #dg-ga #math.DG #msc:53B35 #msc:58F05
paper · pdf · doi:10.48550/arxiv.dg-ga/9605007
LaTex, 26 pages, to appear in Ann. Sci. Ecole Norm. Sup
arxiv created 1996/05/19 · arxiv updated 2009/11/30
The main purpose of the paper is to study hyperkahler structures from the viewpoint of symplectic geometry. We introduce a notion of hypersymplectic structures which encompasses that of hyperkahler structures. Motivated by the work of Kronheimer on (co)adjoint orbits of semi-simple Lie algebras, we define hyper-Lie Poisson structures associated with a compact semi-simple Lie algebra and give criterion which 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 \fraksu(2) are realized as hypersymplectic leaves and are related to the (co)adjoint orbits of \fraksl(2, \complex).