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Article: On the variety of Lagrangian subalgebras, II

TitleOn the variety of Lagrangian subalgebras, II
Authors
Issue Date2006
PublisherElsevier France, Editions Scientifiques et Medicales. The Journal's web site is located at http://www.elsevier.com/locate/ansens
Citation
Annales Scientifiques De L'ecole Normale Superieure, 2006, v. 39 n. 2, p. 347-379 How to Cite?
AbstractMotivated by Drinfeld's theorem on Poisson homogeneous spaces, we study the variety L of Lagrangian subalgebras of g ⊕ g for a complex semi-simple Lie algebra g. Let G be the adjoint group of g. We show that the (G × G)-orbit closures in L are smooth spherical varieties. We also classify the irreducible components of L and show that they are smooth. Using some methods of M. Yakimov, we give a new description and proof of Karolinsky's classification of the diagonal G-orbits in L, which, as a special case, recovers the Belavin-Drinfeld classification of quasi-triangular r-matrices on g. Furthermore, L has a canonical Poisson structure, and we compute its rank at each point and describe its symplectic leaf decomposition in terms of intersections of orbits of two subgroups of G × G. © 2006 Elsevier SAS. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/75255
ISSN
2015 Impact Factor: 1.83
2015 SCImago Journal Rankings: 3.966
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorEvens, Sen_HK
dc.contributor.authorLu, JHen_HK
dc.date.accessioned2010-09-06T07:09:24Z-
dc.date.available2010-09-06T07:09:24Z-
dc.date.issued2006en_HK
dc.identifier.citationAnnales Scientifiques De L'ecole Normale Superieure, 2006, v. 39 n. 2, p. 347-379en_HK
dc.identifier.issn0012-9593en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75255-
dc.description.abstractMotivated by Drinfeld's theorem on Poisson homogeneous spaces, we study the variety L of Lagrangian subalgebras of g ⊕ g for a complex semi-simple Lie algebra g. Let G be the adjoint group of g. We show that the (G × G)-orbit closures in L are smooth spherical varieties. We also classify the irreducible components of L and show that they are smooth. Using some methods of M. Yakimov, we give a new description and proof of Karolinsky's classification of the diagonal G-orbits in L, which, as a special case, recovers the Belavin-Drinfeld classification of quasi-triangular r-matrices on g. Furthermore, L has a canonical Poisson structure, and we compute its rank at each point and describe its symplectic leaf decomposition in terms of intersections of orbits of two subgroups of G × G. © 2006 Elsevier SAS. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherElsevier France, Editions Scientifiques et Medicales. The Journal's web site is located at http://www.elsevier.com/locate/ansensen_HK
dc.relation.ispartofAnnales Scientifiques de l'Ecole Normale Superieureen_HK
dc.titleOn the variety of Lagrangian subalgebras, IIen_HK
dc.typeArticleen_HK
dc.identifier.emailLu, JH:jhluhku@hku.hken_HK
dc.identifier.authorityLu, JH=rp00753en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.ansens.2005.11.004en_HK
dc.identifier.scopuseid_2-s2.0-33744829752en_HK
dc.identifier.hkuros116226en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33744829752&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume39en_HK
dc.identifier.issue2en_HK
dc.identifier.spage347en_HK
dc.identifier.epage379en_HK
dc.identifier.eissn1873-2151-
dc.identifier.isiWOS:000238681800005-
dc.publisher.placeFranceen_HK
dc.identifier.scopusauthoridEvens, S=6601953518en_HK
dc.identifier.scopusauthoridLu, JH=35790078400en_HK

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