Hopf Galois Extensions and Non-commutative Rings

In this document we review the notion of Hopf Galois extensions, addressing remarkable examples, some properties and recent advances in such theory. Similarly, we present some families of non-commutative rings and algebras which arise in several applications and contexts. With particular examples, a...

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Autores:
Calderón Mateus, Fabio Alejandro
Tipo de recurso:
Fecha de publicación:
2019
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/77051
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/77051
http://bdigital.unal.edu.co/74369/
Palabra clave:
Hopf Galois extension
Quantum torsor
Hopf Galois system
Ore extension
Almost symmetric algebra
Extensión Hopf Galois
Torsor cuántico
Sistema Hopf Galois
Extensión de Ore
Algebra casi-simétrica
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_4d6ef44a033688c7703a59af8443cd88
oai_identifier_str oai:repositorio.unal.edu.co:unal/77051
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Reyes Villamil, Milton ArmandoCalderón Mateus, Fabio Alejandro47572be4-6697-4235-9e17-07fe8333de703002020-03-30T06:37:10Z2020-03-30T06:37:10Z2019-04https://repositorio.unal.edu.co/handle/unal/77051http://bdigital.unal.edu.co/74369/In this document we review the notion of Hopf Galois extensions, addressing remarkable examples, some properties and recent advances in such theory. Similarly, we present some families of non-commutative rings and algebras which arise in several applications and contexts. With particular examples, and using recent results on Hopf Galois theory, we study some interactions between such extensions and the mentioned families.Resumen: En este documento abordaremos la noción de extensión Hopf Galois, revisando los ejemplos más destacados, algunas propiedades y los avances recientes en dicha teoría. De igual manera, presentamos algunas familias de anillos y álgebras no-conmutativas que aparecen en diversas aplicaciones y escenarios. Con ejemplos particulares, y usando trabajos recientes en teoría Hopf Galois, estudiamos algunas interacciones entre dichas extensiones y algunas de las familias mencionadas.Maestríaapplication/pdfspaUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de MatemáticasDepartamento de Matemáticas51 Matemáticas / MathematicsCalderón Mateus, Fabio Alejandro (2019) Hopf Galois Extensions and Non-commutative Rings. Maestría thesis, Universidad Nacional de Colombia - Sede Bogotá.Hopf Galois Extensions and Non-commutative RingsTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMHopf Galois extensionQuantum torsorHopf Galois systemOre extensionAlmost symmetric algebraExtensión Hopf GaloisTorsor cuánticoSistema Hopf GaloisExtensión de OreAlgebra casi-simétricaORIGINAL00Tesis.pdfapplication/pdf1265952https://repositorio.unal.edu.co/bitstream/unal/77051/1/00Tesis.pdfbeb1dcc196e7ca318ae61e0242e1686dMD51THUMBNAIL00Tesis.pdf.jpg00Tesis.pdf.jpgGenerated Thumbnailimage/jpeg4065https://repositorio.unal.edu.co/bitstream/unal/77051/2/00Tesis.pdf.jpg4d752b1e52d0a72972fab150287cd5fcMD52unal/77051oai:repositorio.unal.edu.co:unal/770512024-07-15 23:10:07.28Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Hopf Galois Extensions and Non-commutative Rings
title Hopf Galois Extensions and Non-commutative Rings
spellingShingle Hopf Galois Extensions and Non-commutative Rings
Hopf Galois extension
Quantum torsor
Hopf Galois system
Ore extension
Almost symmetric algebra
Extensión Hopf Galois
Torsor cuántico
Sistema Hopf Galois
Extensión de Ore
Algebra casi-simétrica
title_short Hopf Galois Extensions and Non-commutative Rings
title_full Hopf Galois Extensions and Non-commutative Rings
title_fullStr Hopf Galois Extensions and Non-commutative Rings
title_full_unstemmed Hopf Galois Extensions and Non-commutative Rings
title_sort Hopf Galois Extensions and Non-commutative Rings
dc.creator.fl_str_mv Calderón Mateus, Fabio Alejandro
dc.contributor.author.spa.fl_str_mv Calderón Mateus, Fabio Alejandro
dc.contributor.spa.fl_str_mv Reyes Villamil, Milton Armando
dc.subject.proposal.spa.fl_str_mv Hopf Galois extension
Quantum torsor
Hopf Galois system
Ore extension
Almost symmetric algebra
Extensión Hopf Galois
Torsor cuántico
Sistema Hopf Galois
Extensión de Ore
Algebra casi-simétrica
topic Hopf Galois extension
Quantum torsor
Hopf Galois system
Ore extension
Almost symmetric algebra
Extensión Hopf Galois
Torsor cuántico
Sistema Hopf Galois
Extensión de Ore
Algebra casi-simétrica
description In this document we review the notion of Hopf Galois extensions, addressing remarkable examples, some properties and recent advances in such theory. Similarly, we present some families of non-commutative rings and algebras which arise in several applications and contexts. With particular examples, and using recent results on Hopf Galois theory, we study some interactions between such extensions and the mentioned families.
publishDate 2019
dc.date.issued.spa.fl_str_mv 2019-04
dc.date.accessioned.spa.fl_str_mv 2020-03-30T06:37:10Z
dc.date.available.spa.fl_str_mv 2020-03-30T06:37:10Z
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/77051
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/74369/
url https://repositorio.unal.edu.co/handle/unal/77051
http://bdigital.unal.edu.co/74369/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Matemáticas
Departamento de Matemáticas
dc.relation.haspart.spa.fl_str_mv 51 Matemáticas / Mathematics
dc.relation.references.spa.fl_str_mv Calderón Mateus, Fabio Alejandro (2019) Hopf Galois Extensions and Non-commutative Rings. Maestría thesis, Universidad Nacional de Colombia - Sede Bogotá.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/77051/1/00Tesis.pdf
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
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