Group orbits and regular partitions of Poisson manifolds

dc.creatorLu, Jiang-Hua
dc.creatorYakimov, Milen
dc.date2006-09-26
dc.date2007-02-15
dc.date.accessioned2026-07-07T07:46:51Z
dc.date.available2026-07-07T07:46:51Z
dc.descriptionWe study a large class of Poisson manifolds, derived from Manin triples, for which we construct explicit partitions into regular Poisson submanifolds by intersecting certain group orbits. Examples include all varieties ${\mathcal L}$ of Lagrangian subalgebras of reductive quadratic Lie algebras $\d$ with Poisson structures defined by Lagrangian splittings of $\d$. In the special case of $\g \oplus \g$, where $\g$ is a complex semi-simple Lie algebra, we explicitly compute the ranks of the Poisson structures on ${\mathcal L}$ defined by arbitrary Lagrangian splittings of ${\mathfrak g} \oplus {\mathfrak g}$. Such Lagrangian splittings have been classified by P. Delorme, and they contain the Belavin--Drinfeld splittings as special cases.
dc.description23 pages, AMS Latex, minor changes in v.2
dc.identifierhttps://arxiv.org/abs/math/0609732
dc.identifierhttp://arxiv.org/abs/math/0609732
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123964
dc.subjectSymplectic Geometry
dc.subjectRepresentation Theory
dc.titleGroup orbits and regular partitions of Poisson manifolds
dc.typetext

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