Extensions in affine spaces of bilinear applications, differentiable actions, and tensors

Descripción del Articulo

In this article, several generalizations in affine spaces are studied. First, the notion of affine mappings to bilinear mappings defined in affine spaces is explored, referred to as affine bilinear mappings. Subsequently, differentiable actions of a Lie group on affine spaces are defined, and their...

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Detalles Bibliográficos
Autor: Ostos Cordero, Benito Leonardo
Formato: artículo
Fecha de Publicación:2024
Institución:Universidad Nacional de Trujillo
Repositorio:Revistas - Universidad Nacional de Trujillo
Lenguaje:español
OAI Identifier:oai:ojs.revistas.unitru.edu.pe:article/5860
Enlace del recurso:https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5860
Nivel de acceso:acceso abierto
Materia:Affine bilinear
affine action
affine tensor
Bilineal afín
acción afín
tensor afín
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spelling Extensions in affine spaces of bilinear applications, differentiable actions, and tensorsExtensiones en espacios afines de aplicaciones bilineales, acciones diferenciables y tensoresOstos Cordero, Benito LeonardoAffine bilinearaffine actionaffine tensorBilineal afínacción afíntensor afín In this article, several generalizations in affine spaces are studied. First, the notion of affine mappings to bilinear mappings defined in affine spaces is explored, referred to as affine bilinear mappings. Subsequently, differentiable actions of a Lie group on affine spaces are defined, and their isotropy group, orbit space, and set of fixed points are examined. Finally, the concept of tensor product between vector spaces is extended to the tensor product between affine spaces. En este artículo se estudian varias generalizaciones en espacios afines. Primero, se amplía la noción de aplicaciones afines a aplicaciones bilineales definidas en espacios afines, denominadas aplicaciones bilineales afines, y se examinan las formas bilineales afines simétricas y antisimétricas. Luego, se definen acciones diferenciables de un grupo de Lie sobre espacios afines, analizando su grupo de isotropía, su espacio de órbitas y su conjunto de puntos fijos. Finalmente, se extiende la noción de producto tensorial  entre espacios vectoriales a producto tensorial entre espacios afines.National University of Trujillo - Academic Department of Mathematics2024-07-29info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/5860Selecciones Matemáticas; Vol. 11 No. 01 (2024): January - July; 42 - 55Selecciones Matemáticas; Vol. 11 Núm. 01 (2024): Enero - Julio; 42 - 55Selecciones Matemáticas; v. 11 n. 01 (2024): Janeiro - Julho; 42 - 552411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUspahttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/5860/6013Derechos de autor 2024 Selecciones Matemáticashttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/58602024-07-29T16:50:33Z
dc.title.none.fl_str_mv Extensions in affine spaces of bilinear applications, differentiable actions, and tensors
Extensiones en espacios afines de aplicaciones bilineales, acciones diferenciables y tensores
title Extensions in affine spaces of bilinear applications, differentiable actions, and tensors
spellingShingle Extensions in affine spaces of bilinear applications, differentiable actions, and tensors
Ostos Cordero, Benito Leonardo
Affine bilinear
affine action
affine tensor
Bilineal afín
acción afín
tensor afín
title_short Extensions in affine spaces of bilinear applications, differentiable actions, and tensors
title_full Extensions in affine spaces of bilinear applications, differentiable actions, and tensors
title_fullStr Extensions in affine spaces of bilinear applications, differentiable actions, and tensors
title_full_unstemmed Extensions in affine spaces of bilinear applications, differentiable actions, and tensors
title_sort Extensions in affine spaces of bilinear applications, differentiable actions, and tensors
dc.creator.none.fl_str_mv Ostos Cordero, Benito Leonardo
author Ostos Cordero, Benito Leonardo
author_facet Ostos Cordero, Benito Leonardo
author_role author
dc.subject.none.fl_str_mv Affine bilinear
affine action
affine tensor
Bilineal afín
acción afín
tensor afín
topic Affine bilinear
affine action
affine tensor
Bilineal afín
acción afín
tensor afín
description In this article, several generalizations in affine spaces are studied. First, the notion of affine mappings to bilinear mappings defined in affine spaces is explored, referred to as affine bilinear mappings. Subsequently, differentiable actions of a Lie group on affine spaces are defined, and their isotropy group, orbit space, and set of fixed points are examined. Finally, the concept of tensor product between vector spaces is extended to the tensor product between affine spaces.
publishDate 2024
dc.date.none.fl_str_mv 2024-07-29
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5860
url https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5860
dc.language.none.fl_str_mv spa
language spa
dc.relation.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5860/6013
dc.rights.none.fl_str_mv Derechos de autor 2024 Selecciones Matemáticas
https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Derechos de autor 2024 Selecciones Matemáticas
https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
dc.source.none.fl_str_mv Selecciones Matemáticas; Vol. 11 No. 01 (2024): January - July; 42 - 55
Selecciones Matemáticas; Vol. 11 Núm. 01 (2024): Enero - Julio; 42 - 55
Selecciones Matemáticas; v. 11 n. 01 (2024): Janeiro - Julho; 42 - 55
2411-1783
reponame:Revistas - Universidad Nacional de Trujillo
instname:Universidad Nacional de Trujillo
instacron:UNITRU
instname_str Universidad Nacional de Trujillo
instacron_str UNITRU
institution UNITRU
reponame_str Revistas - Universidad Nacional de Trujillo
collection Revistas - Universidad Nacional de Trujillo
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 13.36089
Extensions in affine spaces of bilinear applications, differentiable actions, and tensors
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