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Article: Classical dynamical r-matrices and homogeneous Poisson structures on G/H and K/T

TitleClassical dynamical r-matrices and homogeneous Poisson structures on G/H and K/T
Authors
Issue Date2000
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, 2000, v. 212 n. 2, p. 337-370 How to Cite?
AbstractLet G be a finite dimensional simple complex group equipped with the standard Poisson Lie group structure. We show that all G-homogeneous (holomorphic) Poisson structures on G/H, where H ⊂ G is a Cartan subgroup, come from solutions to the Classical Dynamical Yang-Baxter equations which are classified by Etingof and Varchenko. A similar result holds for a maximal compact subgroup K, and we get a family of K-homogeneous Poisson structures on K/T, where T = K ∩ H is a maximal torus of K. This family exhausts all K-homogeneous Poisson structures on K/T up to isomorphisms. We study some Poisson geometrical properties of members of this family such as their symplectic leaves, their modular classes, and the moment maps for the T-action.
Persistent Identifierhttp://hdl.handle.net/10722/156083
ISSN
2015 Impact Factor: 2.375
2015 SCImago Journal Rankings: 1.760
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLu, JHen_US
dc.date.accessioned2012-08-08T08:40:20Z-
dc.date.available2012-08-08T08:40:20Z-
dc.date.issued2000en_US
dc.identifier.citationCommunications In Mathematical Physics, 2000, v. 212 n. 2, p. 337-370en_US
dc.identifier.issn0010-3616en_US
dc.identifier.urihttp://hdl.handle.net/10722/156083-
dc.description.abstractLet G be a finite dimensional simple complex group equipped with the standard Poisson Lie group structure. We show that all G-homogeneous (holomorphic) Poisson structures on G/H, where H ⊂ G is a Cartan subgroup, come from solutions to the Classical Dynamical Yang-Baxter equations which are classified by Etingof and Varchenko. A similar result holds for a maximal compact subgroup K, and we get a family of K-homogeneous Poisson structures on K/T, where T = K ∩ H is a maximal torus of K. This family exhausts all K-homogeneous Poisson structures on K/T up to isomorphisms. We study some Poisson geometrical properties of members of this family such as their symplectic leaves, their modular classes, and the moment maps for the T-action.en_US
dc.languageengen_US
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00220/index.htmen_US
dc.relation.ispartofCommunications in Mathematical Physicsen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleClassical dynamical r-matrices and homogeneous Poisson structures on G/H and K/Ten_US
dc.typeArticleen_US
dc.identifier.emailLu, JH:jhluhku@hku.hken_US
dc.identifier.authorityLu, JH=rp00753en_US
dc.description.naturepostprinten_US
dc.identifier.doi10.1007/s002200000209-
dc.identifier.scopuseid_2-s2.0-0034349021en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0034349021&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume212en_US
dc.identifier.issue2en_US
dc.identifier.spage337en_US
dc.identifier.epage370en_US
dc.identifier.isiWOS:000088402200005-
dc.publisher.placeGermanyen_US
dc.identifier.scopusauthoridLu, JH=35790078400en_US

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