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Book Chapter: A note on Poisson homogeneous spaces
Title  A note on Poisson homogeneous spaces 

Authors  
Issue Date  2007 
Publisher  University of Luxembourg 
Citation  A note on Poisson homogeneous spaces. In Dito, Giuseppe (Ed.) (Eds.), Poisson geometry in mathematics and physics : international conference, June 59, 2006, Tokyo, Japan, v. 450, p. 173198. Luxembourg: University of Luxembourg, 2007 How to Cite? 
Abstract  We 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 semisimple Lie groups. 
Description  Fulltext link (Postprint): http://arxiv.org/pdf/0706.1337v1.pdf 
Persistent Identifier  http://hdl.handle.net/10722/75295 
ISSN 
DC Field  Value  Language 

dc.contributor.author  Lu, J  en_HK 
dc.date.accessioned  20100906T07:09:46Z   
dc.date.available  20100906T07:09:46Z   
dc.date.issued  2007  en_HK 
dc.identifier.citation  A note on Poisson homogeneous spaces. In Dito, Giuseppe (Ed.) (Eds.), Poisson geometry in mathematics and physics : international conference, June 59, 2006, Tokyo, Japan, v. 450, p. 173198. Luxembourg: University of Luxembourg, 2007  en_HK 
dc.identifier.issn  9782879710921   
dc.identifier.uri  http://hdl.handle.net/10722/75295   
dc.description  Fulltext link (Postprint): http://arxiv.org/pdf/0706.1337v1.pdf   
dc.description.abstract  We 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 semisimple Lie groups.   
dc.language  eng  en_HK 
dc.publisher  University of Luxembourg   
dc.relation.ispartof  Poisson geometry in mathematics and physics : international conference, June 59, 2006, Tokyo, Japan  en_HK 
dc.title  A note on Poisson homogeneous spaces  en_HK 
dc.type  Book_Chapter  en_HK 
dc.identifier.email  Lu, J: jhlu@maths.hku.hk  en_HK 
dc.identifier.authority  Lu, J=rp00753  en_HK 
dc.identifier.hkuros  134973  en_HK 
dc.identifier.volume  450   
dc.identifier.spage  173   
dc.identifier.epage  198   
dc.publisher.place  Luxembourg   