Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2

Autores
Allison, Bruce; Berman, Stephen; Pianzola, Arturo
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let M(n) be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to n-tuples of commuting finite order automorphisms. It is a classical result that M(n) the class of all derived algebras modulo their centres of affine Kac-Moody Lie algebras. This combined with the Peterson-Kac conjugacy theorem for affine algebras results in a classification of the algebras in M(1). In this paper, we classify the algebras in M(2), and further determine the relationship between M(2) and two other classes of Lie algebras: the class of all loop algebras of affine Lie algebras and the class of all extended affine Lie algebras of nullity 2.
Fil: Allison, Bruce. University of Alberta; Canadá
Fil: Berman, Stephen. No especifica;
Fil: Pianzola, Arturo. University of Alberta; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Extended affine Lie algebras
Multiloop algebras
Loop 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:11336/33160
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2Allison, BruceBerman, StephenPianzola, ArturoExtended affine Lie algebrasMultiloop algebrasLoop algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let M(n) be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to n-tuples of commuting finite order automorphisms. It is a classical result that M(n) the class of all derived algebras modulo their centres of affine Kac-Moody Lie algebras. This combined with the Peterson-Kac conjugacy theorem for affine algebras results in a classification of the algebras in M(1). In this paper, we classify the algebras in M(2), and further determine the relationship between M(2) and two other classes of Lie algebras: the class of all loop algebras of affine Lie algebras and the class of all extended affine Lie algebras of nullity 2.Fil: Allison, Bruce. University of Alberta; CanadáFil: Berman, Stephen. No especifica;Fil: Pianzola, Arturo. University of Alberta; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaEuropean Mathematical Society2014-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/33160Pianzola, Arturo; Allison, Bruce; Berman, Stephen; Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2; European Mathematical Society; Journal of the European Mathematical Society; 16; 2; 1-2014; 327-3851435-9855CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4171/JEMS/435info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=16&iss=2&rank=5info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1002.2674info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:41:20Zoai:ri.conicet.gov.ar:11336/33160instacron: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:34982025-11-12 09:41:20.982CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
title Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
spellingShingle Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
Allison, Bruce
Extended affine Lie algebras
Multiloop algebras
Loop algebras
title_short Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
title_full Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
title_fullStr Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
title_full_unstemmed Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
title_sort Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
dc.creator.none.fl_str_mv Allison, Bruce
Berman, Stephen
Pianzola, Arturo
author Allison, Bruce
author_facet Allison, Bruce
Berman, Stephen
Pianzola, Arturo
author_role author
author2 Berman, Stephen
Pianzola, Arturo
author2_role author
author
dc.subject.none.fl_str_mv Extended affine Lie algebras
Multiloop algebras
Loop algebras
topic Extended affine Lie algebras
Multiloop algebras
Loop 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 Let M(n) be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to n-tuples of commuting finite order automorphisms. It is a classical result that M(n) the class of all derived algebras modulo their centres of affine Kac-Moody Lie algebras. This combined with the Peterson-Kac conjugacy theorem for affine algebras results in a classification of the algebras in M(1). In this paper, we classify the algebras in M(2), and further determine the relationship between M(2) and two other classes of Lie algebras: the class of all loop algebras of affine Lie algebras and the class of all extended affine Lie algebras of nullity 2.
Fil: Allison, Bruce. University of Alberta; Canadá
Fil: Berman, Stephen. No especifica;
Fil: Pianzola, Arturo. University of Alberta; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Let M(n) be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to n-tuples of commuting finite order automorphisms. It is a classical result that M(n) the class of all derived algebras modulo their centres of affine Kac-Moody Lie algebras. This combined with the Peterson-Kac conjugacy theorem for affine algebras results in a classification of the algebras in M(1). In this paper, we classify the algebras in M(2), and further determine the relationship between M(2) and two other classes of Lie algebras: the class of all loop algebras of affine Lie algebras and the class of all extended affine Lie algebras of nullity 2.
publishDate 2014
dc.date.none.fl_str_mv 2014-01
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/11336/33160
Pianzola, Arturo; Allison, Bruce; Berman, Stephen; Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2; European Mathematical Society; Journal of the European Mathematical Society; 16; 2; 1-2014; 327-385
1435-9855
CONICET Digital
CONICET
url http://hdl.handle.net/11336/33160
identifier_str_mv Pianzola, Arturo; Allison, Bruce; Berman, Stephen; Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2; European Mathematical Society; Journal of the European Mathematical Society; 16; 2; 1-2014; 327-385
1435-9855
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4171/JEMS/435
info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=16&iss=2&rank=5
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1002.2674
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 European Mathematical Society
publisher.none.fl_str_mv European 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
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score 12.976206

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