Torsors, reductive group schemes and extended affine Lie algebras

Autores
Gille, Philippe; Pianzola, Arturo
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that we take draws heavily for the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows us to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.
Fil: Gille, Philippe. Centre National de la Recherche Scientifique. Ecole Normale Supérieure; Francia
Fil: Pianzola, Arturo. University of Alberta; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Reductive Group Schemes
Loop Torsors
Extended Affine Lie Algebras
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:11336/25470
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/25470
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Torsors, reductive group schemes and extended affine Lie algebrasGille, PhilippePianzola, ArturoReductive Group SchemesLoop TorsorsExtended Affine Lie Algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that we take draws heavily for the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows us to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.Fil: Gille, Philippe. Centre National de la Recherche Scientifique. Ecole Normale Supérieure; FranciaFil: Pianzola, Arturo. University of Alberta; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Mathematical Society2013-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/25470Gille, Philippe; Pianzola, Arturo; Torsors, reductive group schemes and extended affine Lie algebras; American Mathematical Society; Memoirs Of The American Mathematical Society (ams); 226; 1063; 11-2013; 1-1160065-92661947–6221CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1109.3405info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/books/memo/1063/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:47:38Zoai:ri.conicet.gov.ar:11336/25470instacron: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:34982025-09-03 09:47:38.594CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Torsors, reductive group schemes and extended affine Lie algebras
title Torsors, reductive group schemes and extended affine Lie algebras
spellingShingle Torsors, reductive group schemes and extended affine Lie algebras
Gille, Philippe
Reductive Group Schemes
Loop Torsors
Extended Affine Lie Algebras
title_short Torsors, reductive group schemes and extended affine Lie algebras
title_full Torsors, reductive group schemes and extended affine Lie algebras
title_fullStr Torsors, reductive group schemes and extended affine Lie algebras
title_full_unstemmed Torsors, reductive group schemes and extended affine Lie algebras
title_sort Torsors, reductive group schemes and extended affine Lie algebras
dc.creator.none.fl_str_mv Gille, Philippe
Pianzola, Arturo
author Gille, Philippe
author_facet Gille, Philippe
Pianzola, Arturo
author_role author
author2 Pianzola, Arturo
author2_role author
dc.subject.none.fl_str_mv Reductive Group Schemes
Loop Torsors
Extended Affine Lie Algebras
topic Reductive Group Schemes
Loop Torsors
Extended Affine Lie Algebras
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 give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that we take draws heavily for the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows us to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.
Fil: Gille, Philippe. Centre National de la Recherche Scientifique. Ecole Normale Supérieure; Francia
Fil: Pianzola, Arturo. University of Alberta; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that we take draws heavily for the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows us to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.
publishDate 2013
dc.date.none.fl_str_mv 2013-11
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/11336/25470
Gille, Philippe; Pianzola, Arturo; Torsors, reductive group schemes and extended affine Lie algebras; American Mathematical Society; Memoirs Of The American Mathematical Society (ams); 226; 1063; 11-2013; 1-116
0065-9266
1947–6221
CONICET Digital
CONICET
url http://hdl.handle.net/11336/25470
identifier_str_mv Gille, Philippe; Pianzola, Arturo; Torsors, reductive group schemes and extended affine Lie algebras; American Mathematical Society; Memoirs Of The American Mathematical Society (ams); 226; 1063; 11-2013; 1-116
0065-9266
1947–6221
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://arxiv.org/abs/1109.3405
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/books/memo/1063/
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 American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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_ 1842268872662581248
score 13.13397

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