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Conference Paper: A note on Poisson homogeneous spaces

TitleA note on Poisson homogeneous spaces
Authors
Issue Date2008
PublisherAmerican Mathematical Society
Citation
Poisson geometry in mathematics and physics: international conference, Tokyo, Japan, 5-9 June 2006. In Contemporary Mathematics (American Mathematical Society), 2008, v. 450, p. 173-198 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.
DescriptionConference Proceeding
Persistent Identifierhttp://hdl.handle.net/10722/75295
ISBN

 

DC FieldValueLanguage
dc.contributor.authorLu, Jen_HK
dc.date.accessioned2010-09-06T07:09:46Z-
dc.date.available2010-09-06T07:09:46Z-
dc.date.issued2008en_HK
dc.identifier.citationPoisson geometry in mathematics and physics: international conference, Tokyo, Japan, 5-9 June 2006. In Contemporary Mathematics (American Mathematical Society), 2008, v. 450, p. 173-198en_HK
dc.identifier.isbn9780821844236-
dc.identifier.urihttp://hdl.handle.net/10722/75295-
dc.descriptionConference Proceeding-
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.publisherAmerican Mathematical Society-
dc.relation.ispartofContemporary Mathematics (American Mathematical Society)en_HK
dc.rightsFirst published in [Contemporary mathematics] in [2018, volume 450], published by the American Mathematical Society-
dc.titleA note on Poisson homogeneous spacesen_HK
dc.typeConference_Paperen_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.placeUnited States-

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