On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras

Autores
Cagliero, Leandro Roberto; Szchetman, Fernando
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,yin K$. When is $F[x,y]=F[alpha x+eta y]$ for some non-zero elements $alpha,etain F$?
Fil: Cagliero, Leandro Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Szchetman, Fernando. University of Regina; Canadá
Materia
Uniserial Module
Lie Algebra
Associative Algebra
Primitive Element
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:11336/32141
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/32141
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network_name_str CONICET Digital (CONICET)
spelling On the theorem of the primitive element with applications to the representation theory of associative and Lie algebrasCagliero, Leandro RobertoSzchetman, FernandoUniserial ModuleLie AlgebraAssociative AlgebraPrimitive Elementhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,yin K$. When is $F[x,y]=F[alpha x+eta y]$ for some non-zero elements $alpha,etain F$?Fil: Cagliero, Leandro Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Szchetman, Fernando. University of Regina; CanadáCanadian Mathematical Soc2014-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/32141Cagliero, Leandro Roberto; Szchetman, Fernando; On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras; Canadian Mathematical Soc; Canadian Mathematical Bulletin-bulletin Canadien de Mathematiques; 57; 12-2014; 735-7480008-4395CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1306.3965info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/on-the-theorem-of-the-primitive-element-with-applications-to-the-representation-theory-of-associative-and-lie-algebras/D8877328E0421D85BB4D0FC2A1181C1Ainfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:08:58Zoai:ri.conicet.gov.ar:11336/32141instacron: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 11:08:58.934CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
title On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
spellingShingle On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
Cagliero, Leandro Roberto
Uniserial Module
Lie Algebra
Associative Algebra
Primitive Element
title_short On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
title_full On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
title_fullStr On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
title_full_unstemmed On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
title_sort On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
dc.creator.none.fl_str_mv Cagliero, Leandro Roberto
Szchetman, Fernando
author Cagliero, Leandro Roberto
author_facet Cagliero, Leandro Roberto
Szchetman, Fernando
author_role author
author2 Szchetman, Fernando
author2_role author
dc.subject.none.fl_str_mv Uniserial Module
Lie Algebra
Associative Algebra
Primitive Element
topic Uniserial Module
Lie Algebra
Associative Algebra
Primitive Element
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 describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,yin K$. When is $F[x,y]=F[alpha x+eta y]$ for some non-zero elements $alpha,etain F$?
Fil: Cagliero, Leandro Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Szchetman, Fernando. University of Regina; Canadá
description We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,yin K$. When is $F[x,y]=F[alpha x+eta y]$ for some non-zero elements $alpha,etain F$?
publishDate 2014
dc.date.none.fl_str_mv 2014-12
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/11336/32141
Cagliero, Leandro Roberto; Szchetman, Fernando; On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras; Canadian Mathematical Soc; Canadian Mathematical Bulletin-bulletin Canadien de Mathematiques; 57; 12-2014; 735-748
0008-4395
CONICET Digital
CONICET
url http://hdl.handle.net/11336/32141
identifier_str_mv Cagliero, Leandro Roberto; Szchetman, Fernando; On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras; Canadian Mathematical Soc; Canadian Mathematical Bulletin-bulletin Canadien de Mathematiques; 57; 12-2014; 735-748
0008-4395
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1306.3965
info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/on-the-theorem-of-the-primitive-element-with-applications-to-the-representation-theory-of-associative-and-lie-algebras/D8877328E0421D85BB4D0FC2A1181C1A
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 Canadian Mathematical Soc
publisher.none.fl_str_mv Canadian Mathematical Soc
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 12.8982525

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