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Article: Group orbits and regular partitions of poisson manifolds

TitleGroup orbits and regular partitions of poisson manifolds
Authors
Issue Date2008
PublisherSpringer 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?
AbstractWe 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 Identifierhttp://hdl.handle.net/10722/58961
ISSN
2015 Impact Factor: 2.375
2015 SCImago Journal Rankings: 1.760
ISI Accession Number ID
Funding AgencyGrant Number
HKRGC703304
703405
NSFDMS-0406057
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 FieldValueLanguage
dc.contributor.authorLu, JHen_HK
dc.contributor.authorYakimov, Men_HK
dc.date.accessioned2010-05-31T03:40:25Z-
dc.date.available2010-05-31T03:40:25Z-
dc.date.issued2008en_HK
dc.identifier.citationCommunications In Mathematical Physics, 2008, v. 283 n. 3, p. 729-748en_HK
dc.identifier.issn0010-3616en_HK
dc.identifier.urihttp://hdl.handle.net/10722/58961-
dc.description.abstractWe 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.languageengen_HK
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00220/index.htmen_HK
dc.relation.ispartofCommunications in Mathematical Physicsen_HK
dc.titleGroup orbits and regular partitions of poisson manifoldsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://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+Manifoldsen_HK
dc.identifier.emailLu, JH:jhluhku@hku.hken_HK
dc.identifier.authorityLu, JH=rp00753en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s00220-008-0536-zen_HK
dc.identifier.scopuseid_2-s2.0-50249183955en_HK
dc.identifier.hkuros154298en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-50249183955&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume283en_HK
dc.identifier.issue3en_HK
dc.identifier.spage729en_HK
dc.identifier.epage748en_HK
dc.identifier.eissn1432-0916-
dc.identifier.isiWOS:000258672500007-
dc.publisher.placeGermanyen_HK
dc.identifier.scopusauthoridLu, JH=35790078400en_HK
dc.identifier.scopusauthoridYakimov, M=8377528700en_HK

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