On the classification of Lie bialgebras by cohomological means

Autores
Alsaody, Seidon; Pianzola, Arturo
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint of descent and non-abelian cohomology. We achieve a description of the problem in terms of faithfully flat cohomology over an arbitrary ring over Q, and solve it for Drinfeld–Jimbo Lie bialgebras over fields of characteristic zero. We consider the classification up to isomorphism, as opposed to equivalence, and treat split and non-split Lie algebras alike. We moreover give a new interpretation of scalar multiples of Lie bialgebras hitherto studied using twisted Belavin–Drinfeld cohomology.
Fil: Alsaody, Seidon. University of Alberta; Canadá
Fil: Pianzola, Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. University of Alberta; Canadá
Materia
Lie Bialgebra
Galois Cohomology
Drinfeld-Jimbo
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/175449
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/175449
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network_name_str CONICET Digital (CONICET)
spelling On the classification of Lie bialgebras by cohomological meansAlsaody, SeidonPianzola, ArturoLie BialgebraGalois CohomologyDrinfeld-Jimbohttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint of descent and non-abelian cohomology. We achieve a description of the problem in terms of faithfully flat cohomology over an arbitrary ring over Q, and solve it for Drinfeld–Jimbo Lie bialgebras over fields of characteristic zero. We consider the classification up to isomorphism, as opposed to equivalence, and treat split and non-split Lie algebras alike. We moreover give a new interpretation of scalar multiples of Lie bialgebras hitherto studied using twisted Belavin–Drinfeld cohomology.Fil: Alsaody, Seidon. University of Alberta; CanadáFil: Pianzola, Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. University of Alberta; CanadáUniversität Bielefeld2019-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/175449Alsaody, Seidon; Pianzola, Arturo; On the classification of Lie bialgebras by cohomological means; Universität Bielefeld; Documenta Mathematica; 24; 11-2019; 2583-26121431-0643CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.elibm.org/ft/10012013000info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:44:23Zoai:ri.conicet.gov.ar:11336/175449instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:44:23.597CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the classification of Lie bialgebras by cohomological means
title On the classification of Lie bialgebras by cohomological means
spellingShingle On the classification of Lie bialgebras by cohomological means
Alsaody, Seidon
Lie Bialgebra
Galois Cohomology
Drinfeld-Jimbo
title_short On the classification of Lie bialgebras by cohomological means
title_full On the classification of Lie bialgebras by cohomological means
title_fullStr On the classification of Lie bialgebras by cohomological means
title_full_unstemmed On the classification of Lie bialgebras by cohomological means
title_sort On the classification of Lie bialgebras by cohomological means
dc.creator.none.fl_str_mv Alsaody, Seidon
Pianzola, Arturo
author Alsaody, Seidon
author_facet Alsaody, Seidon
Pianzola, Arturo
author_role author
author2 Pianzola, Arturo
author2_role author
dc.subject.none.fl_str_mv Lie Bialgebra
Galois Cohomology
Drinfeld-Jimbo
topic Lie Bialgebra
Galois Cohomology
Drinfeld-Jimbo
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint of descent and non-abelian cohomology. We achieve a description of the problem in terms of faithfully flat cohomology over an arbitrary ring over Q, and solve it for Drinfeld–Jimbo Lie bialgebras over fields of characteristic zero. We consider the classification up to isomorphism, as opposed to equivalence, and treat split and non-split Lie algebras alike. We moreover give a new interpretation of scalar multiples of Lie bialgebras hitherto studied using twisted Belavin–Drinfeld cohomology.
Fil: Alsaody, Seidon. University of Alberta; Canadá
Fil: Pianzola, Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. University of Alberta; Canadá
description We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint of descent and non-abelian cohomology. We achieve a description of the problem in terms of faithfully flat cohomology over an arbitrary ring over Q, and solve it for Drinfeld–Jimbo Lie bialgebras over fields of characteristic zero. We consider the classification up to isomorphism, as opposed to equivalence, and treat split and non-split Lie algebras alike. We moreover give a new interpretation of scalar multiples of Lie bialgebras hitherto studied using twisted Belavin–Drinfeld cohomology.
publishDate 2019
dc.date.none.fl_str_mv 2019-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/175449
Alsaody, Seidon; Pianzola, Arturo; On the classification of Lie bialgebras by cohomological means; Universität Bielefeld; Documenta Mathematica; 24; 11-2019; 2583-2612
1431-0643
CONICET Digital
CONICET
url http://hdl.handle.net/11336/175449
identifier_str_mv Alsaody, Seidon; Pianzola, Arturo; On the classification of Lie bialgebras by cohomological means; Universität Bielefeld; Documenta Mathematica; 24; 11-2019; 2583-2612
1431-0643
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.elibm.org/ft/10012013000
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universität Bielefeld
publisher.none.fl_str_mv Universität Bielefeld
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846083546775552000
score 13.22299

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