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Article: Group orbits and regular partitions of poisson manifolds
| Title | Group orbits and regular partitions of poisson manifolds | ||||||
|---|---|---|---|---|---|---|---|
| Authors | |||||||
| Issue Date | 2008 | ||||||
| Publisher | Springer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00220/index.htm | ||||||
| Citation | Communications In Mathematical Physics, 2008, v. 283 n. 3, p. 729-748 How to Cite? | ||||||
| Abstract | We 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 L of Lagrangian subalgebras of reductive quadratic Lie algebras a with Poisson structures defined by Lagrangian splittings of a. In the special case g ⊕ g, where g is a complex semi-simple Lie algebra, we explicitly compute the ranks of the Poisson structures on L defined by arbitrary Lagrangian splittings of g ⊕ g. Such Lagrangian splittings have been classified by P. Delorme, and they contain the Belavin-Drinfeld splittings as special cases. © 2008 Springer-Verlag. | ||||||
| Persistent Identifier | http://hdl.handle.net/10722/58961 | ||||||
| ISSN | 2023 Impact Factor: 2.2 2023 SCImago Journal Rankings: 1.612 | ||||||
| ISI Accession Number ID |
Funding Information: The second author would like to thank the University of Hong Kong for the warm hospitality during his visits in March 2004 and August 2005 when this work was initiated. The first author would like to thank UC Santa Barbara for her visit in July 2006 during which the paper took its final form. We would also like to thank Xuhua He for a key argument in the proof of Proposition 4.4. The first author was partially supported by HKRGC grants 703304 and 703405, and the second author by NSF grant DMS-0406057 and an Alfred P. Sloan research fellowship. | ||||||
| References |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Lu, JH | en_HK |
| dc.contributor.author | Yakimov, M | en_HK |
| dc.date.accessioned | 2010-05-31T03:40:25Z | - |
| dc.date.available | 2010-05-31T03:40:25Z | - |
| dc.date.issued | 2008 | en_HK |
| dc.identifier.citation | Communications In Mathematical Physics, 2008, v. 283 n. 3, p. 729-748 | en_HK |
| dc.identifier.issn | 0010-3616 | en_HK |
| dc.identifier.uri | http://hdl.handle.net/10722/58961 | - |
| dc.description.abstract | We 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 L of Lagrangian subalgebras of reductive quadratic Lie algebras a with Poisson structures defined by Lagrangian splittings of a. In the special case g ⊕ g, where g is a complex semi-simple Lie algebra, we explicitly compute the ranks of the Poisson structures on L defined by arbitrary Lagrangian splittings of g ⊕ g. Such Lagrangian splittings have been classified by P. Delorme, and they contain the Belavin-Drinfeld splittings as special cases. © 2008 Springer-Verlag. | en_HK |
| dc.language | eng | en_HK |
| dc.publisher | Springer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00220/index.htm | en_HK |
| dc.relation.ispartof | Communications in Mathematical Physics | en_HK |
| dc.title | Group orbits and regular partitions of poisson manifolds | en_HK |
| dc.type | Article | en_HK |
| dc.identifier.openurl | http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0010-3616&volume=283&issue=3&spage=729&epage=748&date=2008&atitle=Group+Orbits+and+Regular+Partitions+of+Poisson+Manifolds | en_HK |
| dc.identifier.email | Lu, JH:jhluhku@hku.hk | en_HK |
| dc.identifier.authority | Lu, JH=rp00753 | en_HK |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1007/s00220-008-0536-z | en_HK |
| dc.identifier.scopus | eid_2-s2.0-50249183955 | en_HK |
| dc.identifier.hkuros | 154298 | en_HK |
| dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-50249183955&selection=ref&src=s&origin=recordpage | en_HK |
| dc.identifier.volume | 283 | en_HK |
| dc.identifier.issue | 3 | en_HK |
| dc.identifier.spage | 729 | en_HK |
| dc.identifier.epage | 748 | en_HK |
| dc.identifier.eissn | 1432-0916 | - |
| dc.identifier.isi | WOS:000258672500007 | - |
| dc.publisher.place | Germany | en_HK |
| dc.identifier.scopusauthorid | Lu, JH=35790078400 | en_HK |
| dc.identifier.scopusauthorid | Yakimov, M=8377528700 | en_HK |
| dc.identifier.issnl | 0010-3616 | - |