Abstract
The main purpose of the paper is to study hyperkähler structures from the viewpoint of symplectic geometry. We introduce a notion of hypersymplectic structures which encompasses that of hyperkähler structures. Motivated by the work of Kronheimer on (co)adjoint orbits of semi-simple Lie algebras [10], [11], 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 su(2) are realized as hypersymplectic leaves and are related to the (co)adjoint orbits of sl(2,).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Annales scientifiques de l'Ecole normale superieure
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
