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Book Chapter: A note on Poisson homogeneous spaces

TitleA note on Poisson homogeneous spaces
Authors
Issue Date2007
PublisherUniversity of Luxembourg
Citation
A note on Poisson homogeneous spaces. In Dito, Giuseppe (Ed.) (Eds.), Poisson geometry in mathematics and physics : international conference, June 5-9, 2006, Tokyo, Japan, v. 450, p. 173-198. Luxembourg: University of Luxembourg, 2007 How to Cite?
AbstractWe 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.
DescriptionFulltext link (Postprint): http://arxiv.org/pdf/0706.1337v1.pdf
Persistent Identifierhttp://hdl.handle.net/10722/75295
ISSN

 

DC FieldValueLanguage
dc.contributor.authorLu, Jen_HK
dc.date.accessioned2010-09-06T07:09:46Z-
dc.date.available2010-09-06T07:09:46Z-
dc.date.issued2007en_HK
dc.identifier.citationA note on Poisson homogeneous spaces. In Dito, Giuseppe (Ed.) (Eds.), Poisson geometry in mathematics and physics : international conference, June 5-9, 2006, Tokyo, Japan, v. 450, p. 173-198. Luxembourg: University of Luxembourg, 2007en_HK
dc.identifier.issn9782879710921-
dc.identifier.urihttp://hdl.handle.net/10722/75295-
dc.descriptionFulltext link (Postprint): http://arxiv.org/pdf/0706.1337v1.pdf-
dc.description.abstractWe 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.languageengen_HK
dc.publisherUniversity of Luxembourg-
dc.relation.ispartofPoisson geometry in mathematics and physics : international conference, June 5-9, 2006, Tokyo, Japanen_HK
dc.titleA note on Poisson homogeneous spacesen_HK
dc.typeBook_Chapteren_HK
dc.identifier.emailLu, J: jhlu@maths.hku.hken_HK
dc.identifier.authorityLu, J=rp00753en_HK
dc.identifier.hkuros134973en_HK
dc.identifier.volume450-
dc.identifier.spage173-
dc.identifier.epage198-
dc.publisher.placeLuxembourg-

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