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Article: On the variety of Lagrangian subalgebras, I

TitleOn the variety of Lagrangian subalgebras, I
Authors
Evens, SLu, JH
Issue Date2001
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, 2001, v. 34 n. 5, p. 631-668 How to Cite?
DOI: http://dx.doi.org/10.1016/S0012-9593(01)01072-2
AbstractWe study subalgebras of a semi-simple Lie algebra which are Lagrangian with respect to the imaginary part of the Killing form. We show that the variety L of Lagrangian subalgebras carries a natural Poisson structure Π. We determine the irreducible components of L, and we show that each irreducible component is a smooth fiber bundle over a generalized flag variety, and that the fiber is the product of the set of real points of a De Concini-Procesi compactification and a connected component of a real orthogonal group. We study some properties of the Poisson structure Π and show that L contains many interesting Poisson submanifolds. © 2001 Éditions scientifiques et médicales Elsevier SAS.
Persistent Identifierhttp://hdl.handle.net/10722/156052
ISSN
0012-9593
2023 Impact Factor: 1.3
2023 SCImago Journal Rankings: 2.419
ISI Accession Number ID
WOS:000172445400001
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorEvens, Sen_US
dc.contributor.authorLu, JHen_US
dc.date.accessioned2012-08-08T08:40:12Z-
dc.date.available2012-08-08T08:40:12Z-
dc.date.issued2001en_US
dc.identifier.citationAnnales Scientifiques De L'ecole Normale Superieure, 2001, v. 34 n. 5, p. 631-668en_US
dc.identifier.issn0012-9593en_US
dc.identifier.urihttp://hdl.handle.net/10722/156052-
dc.description.abstractWe study subalgebras of a semi-simple Lie algebra which are Lagrangian with respect to the imaginary part of the Killing form. We show that the variety L of Lagrangian subalgebras carries a natural Poisson structure Π. We determine the irreducible components of L, and we show that each irreducible component is a smooth fiber bundle over a generalized flag variety, and that the fiber is the product of the set of real points of a De Concini-Procesi compactification and a connected component of a real orthogonal group. We study some properties of the Poisson structure Π and show that L contains many interesting Poisson submanifolds. © 2001 Éditions scientifiques et médicales Elsevier SAS.en_US
dc.languageengen_US
dc.publisherElsevier France, Editions Scientifiques et Medicales. The Journal's web site is located at http://www.elsevier.com/locate/ansensen_US
dc.relation.ispartofAnnales Scientifiques de l'Ecole Normale Superieureen_US
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.titleOn the variety of Lagrangian subalgebras, Ien_US
dc.typeArticleen_US
dc.identifier.emailLu, JH:jhluhku@hku.hken_US
dc.identifier.authorityLu, JH=rp00753en_US
dc.description.naturepostprinten_US
dc.identifier.doi10.1016/S0012-9593(01)01072-2en_US
dc.identifier.scopuseid_2-s2.0-0013355981en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0013355981&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume34en_US
dc.identifier.issue5en_US
dc.identifier.spage631en_US
dc.identifier.epage668en_US
dc.identifier.isiWOS:000172445400001-
dc.publisher.placeFranceen_US
dc.identifier.scopusauthoridEvens, S=6601953518en_US
dc.identifier.scopusauthoridLu, JH=35790078400en_US
dc.identifier.issnl0012-9593-

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