Spin geometry and orthogonal groups

"In this work, we study Clifford algebras, motivated by the very geometrical problem of finding non-vanishing vector fields over the sphere. The study of such algebras naturally leads to Spin groups which are proven to be the universal covering of the orthogonal groups. We classify Clifford alg...

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Autores:: Jaramillo Duque, David

Tipo de recurso:: Trabajo de grado de pregrado

Fecha de publicación:: 2017

Institución:: Universidad de los Andes

Repositorio:: Séneca: repositorio Uniandes

Idioma:: eng

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spelling	Al consultar y hacer uso de este recurso, está aceptando las condiciones de uso establecidas por los autores.http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Schaffhauser, Florent8ee887f6-cc38-42d0-af3d-ba696ba4229e500Jaramillo Duque, Davidefe8c050-a6f8-4a04-8c51-41255c2e801c4002022-09-26T22:28:08Z2022-09-26T22:28:08Z2017http://hdl.handle.net/1992/61606instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/795326-1001"In this work, we study Clifford algebras, motivated by the very geometrical problem of finding non-vanishing vector fields over the sphere. The study of such algebras naturally leads to Spin groups which are proven to be the universal covering of the orthogonal groups. We classify Clifford algebras and describe their relation to Spin groups. Studying the irreducible representations of Clifford algebras we get interesting isomorphisms for low dimensional Spin groups. And, at the very end, with the machinery developed we study the construction of non-vanishing vector fields over the sphere and the projective space." -- Tomado del Formato de Documento de Grado."En este trabajo, estudiamos álgebras de Clifford, motivados por el problema geométrico de hallar campos vectoriales que no se anulen sobre la esfera. El estudio de algebras de Clifford naturalmente nos lleva a considerar los grupos de Spin, de los cuáles se prueba que son el recubrimiento universal de los grupos ortogonales. Clasificamos las álgebras de Clifford y describimos sus relaciones con los grupos de Spin. Estudiando las representaciones irreducibles de álgebras de Clifford obtuvimos isomorfismos interesantes para los grupos de Spin en dimensión baja. Al final, utilizando las herramientas construidas, estudiamos la construcción de campos vectoriales que no se anulan sobre las esferas y los espacios proyectivos." -- Tomado del Formato de Documento de Grado.MatemáticoPregrado44 hojasapplication/pdfengUniversidad de los AndesMatemáticasFacultad de CienciasDepartamento de MatemáticasSpin geometry and orthogonal groupsTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_7a1fTexthttp://purl.org/redcol/resource_type/TPAlgebras de CliffordAnálisis espinorialRepresentación de grupos (Matemáticas)Geometría de giro201127233PublicationTEXT12627.pdf.txt12627.pdf.txtExtracted texttext/plain60406https://repositorio.uniandes.edu.co/bitstreams/e05b343b-a5d7-4f81-9d35-cba544491ba2/downloadd089746ed86380a53191f46aa48b7c4bMD52THUMBNAIL12627.pdf.jpg12627.pdf.jpgIM Thumbnailimage/jpeg7329https://repositorio.uniandes.edu.co/bitstreams/28ab126f-79f5-4300-97a2-f2374704aba8/download89fc7b24425797f5442d4e538053cf54MD53ORIGINAL12627.pdfapplication/pdf294706https://repositorio.uniandes.edu.co/bitstreams/fedb8436-e0f6-4de6-8f4e-0751ec2956ac/downloadf34608c660a93c3a4390f6d3cec0855aMD511992/61606oai:repositorio.uniandes.edu.co:1992/616062023-10-10 19:49:29.971http://creativecommons.org/licenses/by-nc-sa/4.0/open.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.co
dc.title.spa.fl_str_mv	Spin geometry and orthogonal groups
title	Spin geometry and orthogonal groups
spellingShingle	Spin geometry and orthogonal groups Algebras de Clifford Análisis espinorial Representación de grupos (Matemáticas) Geometría de giro
title_short	Spin geometry and orthogonal groups
title_full	Spin geometry and orthogonal groups
title_fullStr	Spin geometry and orthogonal groups
title_full_unstemmed	Spin geometry and orthogonal groups
title_sort	Spin geometry and orthogonal groups
dc.creator.fl_str_mv	Jaramillo Duque, David
dc.contributor.advisor.none.fl_str_mv	Schaffhauser, Florent
dc.contributor.author.none.fl_str_mv	Jaramillo Duque, David
dc.subject.keyword.spa.fl_str_mv	Algebras de Clifford Análisis espinorial Representación de grupos (Matemáticas) Geometría de giro
topic	Algebras de Clifford Análisis espinorial Representación de grupos (Matemáticas) Geometría de giro
description	"In this work, we study Clifford algebras, motivated by the very geometrical problem of finding non-vanishing vector fields over the sphere. The study of such algebras naturally leads to Spin groups which are proven to be the universal covering of the orthogonal groups. We classify Clifford algebras and describe their relation to Spin groups. Studying the irreducible representations of Clifford algebras we get interesting isomorphisms for low dimensional Spin groups. And, at the very end, with the machinery developed we study the construction of non-vanishing vector fields over the sphere and the projective space." -- Tomado del Formato de Documento de Grado.
publishDate	2017
dc.date.issued.spa.fl_str_mv	2017
dc.date.accessioned.none.fl_str_mv	2022-09-26T22:28:08Z
dc.date.available.none.fl_str_mv	2022-09-26T22:28:08Z
dc.type.spa.fl_str_mv	Trabajo de grado - Pregrado
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dc.language.iso.spa.fl_str_mv	eng
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dc.format.extent.spa.fl_str_mv	44 hojas
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dc.publisher.spa.fl_str_mv	Universidad de los Andes
dc.publisher.program.spa.fl_str_mv	Matemáticas
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.department.spa.fl_str_mv	Departamento de Matemáticas
institution	Universidad de los Andes
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Spin geometry and orthogonal groups

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