Maximal ideals and representations of twisted forms of algebras

Autores
Lau, Michael; Pianzola, Arturo
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Abstract Given a central simple algebra g g and a Galois extension of base rings S ∕ R S∕R, we show that the maximal ideals of twisted S ∕ R S∕R-forms of the algebra of currents g ( R ) g(R) are in natural bijection with the maximal ideals of R R. When g g is a Lie algebra, we use this to give a complete classification of the finite-dimensional simple modules over twisted forms of g ( R ) g(R).
Fil: Lau, Michael. Laval University; Canadá
Fil: Pianzola, Arturo. University of Alberta; Canadá. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Galois descent
Maximal ideal
Twisted forms of 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:11336/27458
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Maximal ideals and representations of twisted forms of algebrasLau, MichaelPianzola, ArturoGalois descentMaximal idealTwisted forms of algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Abstract Given a central simple algebra g g and a Galois extension of base rings S ∕ R S∕R, we show that the maximal ideals of twisted S ∕ R S∕R-forms of the algebra of currents g ( R ) g(R) are in natural bijection with the maximal ideals of R R. When g g is a Lie algebra, we use this to give a complete classification of the finite-dimensional simple modules over twisted forms of g ( R ) g(R).Fil: Lau, Michael. Laval University; CanadáFil: Pianzola, Arturo. University of Alberta; Canadá. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaMathematical Sciences Publishers2013-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/27458Lau, Michael; Pianzola, Arturo; Maximal ideals and representations of twisted forms of algebras; Mathematical Sciences Publishers; Algebra & Number Theory; 7; 2; 7-2013; 431-4481937-06521944-7833CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.2140/ant.2013.7.431info:eu-repo/semantics/altIdentifier/url/https://msp.org/ant/2013/7-2/p07.xhtmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:57:13Zoai:ri.conicet.gov.ar:11336/27458instacron: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:34982025-10-22 11:57:14.097CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Maximal ideals and representations of twisted forms of algebras
title Maximal ideals and representations of twisted forms of algebras
spellingShingle Maximal ideals and representations of twisted forms of algebras
Lau, Michael
Galois descent
Maximal ideal
Twisted forms of algebras
title_short Maximal ideals and representations of twisted forms of algebras
title_full Maximal ideals and representations of twisted forms of algebras
title_fullStr Maximal ideals and representations of twisted forms of algebras
title_full_unstemmed Maximal ideals and representations of twisted forms of algebras
title_sort Maximal ideals and representations of twisted forms of algebras
dc.creator.none.fl_str_mv Lau, Michael
Pianzola, Arturo
author Lau, Michael
author_facet Lau, Michael
Pianzola, Arturo
author_role author
author2 Pianzola, Arturo
author2_role author
dc.subject.none.fl_str_mv Galois descent
Maximal ideal
Twisted forms of algebras
topic Galois descent
Maximal ideal
Twisted forms of 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 Abstract Given a central simple algebra g g and a Galois extension of base rings S ∕ R S∕R, we show that the maximal ideals of twisted S ∕ R S∕R-forms of the algebra of currents g ( R ) g(R) are in natural bijection with the maximal ideals of R R. When g g is a Lie algebra, we use this to give a complete classification of the finite-dimensional simple modules over twisted forms of g ( R ) g(R).
Fil: Lau, Michael. Laval University; Canadá
Fil: Pianzola, Arturo. University of Alberta; Canadá. Universidad Centro de Altos Estudios en Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Abstract Given a central simple algebra g g and a Galois extension of base rings S ∕ R S∕R, we show that the maximal ideals of twisted S ∕ R S∕R-forms of the algebra of currents g ( R ) g(R) are in natural bijection with the maximal ideals of R R. When g g is a Lie algebra, we use this to give a complete classification of the finite-dimensional simple modules over twisted forms of g ( R ) g(R).
publishDate 2013
dc.date.none.fl_str_mv 2013-07
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/11336/27458
Lau, Michael; Pianzola, Arturo; Maximal ideals and representations of twisted forms of algebras; Mathematical Sciences Publishers; Algebra & Number Theory; 7; 2; 7-2013; 431-448
1937-0652
1944-7833
CONICET Digital
CONICET
url http://hdl.handle.net/11336/27458
identifier_str_mv Lau, Michael; Pianzola, Arturo; Maximal ideals and representations of twisted forms of algebras; Mathematical Sciences Publishers; Algebra & Number Theory; 7; 2; 7-2013; 431-448
1937-0652
1944-7833
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.2140/ant.2013.7.431
info:eu-repo/semantics/altIdentifier/url/https://msp.org/ant/2013/7-2/p07.xhtml
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 Mathematical Sciences Publishers
publisher.none.fl_str_mv Mathematical Sciences Publishers
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 12.982451

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