A note on Poisson homogeneous spaces

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dc.creatorLu, Jiang-Hua
dc.date2007-06-10
dc.date.accessioned2026-07-07T08:04:49Z
dc.date.available2026-07-07T08:04:49Z
dc.descriptionWe identify the cotangent bundle Lie algebroid of a Poisson homogeneous space G/H of a Poisson Lie group G as a quotient of a transformation Lie algebroid over G. As applications, we describe the modular vector fields of G/H, and we identify the Poisson cohomology of G/H with coefficients in powers of its canonical line bundle with relative Lie algebra cohomology of the Drinfeld Lie algebra associated to G/H. We also construct a Poisson groupoid over G/H which is symplectic near the identity section. This note serves as preparation for forthcoming papers, in which we will compute explicitly the Poisson cohomology and study their symplectic groupoids for certain examples of Poisson homogeneous spaces related to semi-simple Lie groups.
dc.identifierhttps://arxiv.org/abs/0706.1337
dc.identifierhttp://arxiv.org/abs/0706.1337
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130103
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.titleA note on Poisson homogeneous spaces
dc.typetext

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