Hyper-Lie Poisson structures

Research output: Contribution to journalArticle

7 Citations (Scopus)

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, ℂ).

Original languageEnglish (US)
Pages (from-to)279-302
Number of pages24
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume30
Issue number3
DOIs
StatePublished - Jan 1 1997

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Poisson Structure
Coadjoint Orbits
Semisimple Lie Algebra
Symplectic Geometry
Moduli Space
Lie Algebra
Leaves
Imply

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "The main purpose of the paper is to study hyperk{\"a}hler structures from the viewpoint of symplectic geometry. We introduce a notion of hypersymplectic structures which encompasses that of hyperk{\"a}hler 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, ℂ).",
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Hyper-Lie Poisson structures. / Xu, Ping.

In: Annales Scientifiques de l'Ecole Normale Superieure, Vol. 30, No. 3, 01.01.1997, p. 279-302.

Research output: Contribution to journalArticle

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