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Previous issue date: 2013-08-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this paper, we study Clifford algebras so universal and constructive as quantization of
exterior algebra, we classify all Clifford algebras associated with the quadratic Minkowski
spaces (Rp+q, p,q), where p,q(u) = u21
+...+u2
p −(u2
p+1 +...+u2
p+q), u = (u1, ..., up+q) ∈
Rp+q, which we denote by Clp,q, as well as their complexifications. To do so, we use
important results as the periodicity theorem Carton / Bott. The, we study their representations,
emphasizing the Twisted Adjoint Representataion, Spin Representation and
the Spin-Half Representation moreover using the number of Radon-Hurwitz we study
representations of the algebras Cl0,k. / Neste trabalho, estudamos as ´algebras de Clifford Cl(V, ) associadas aos espa¸cos quadr´aticos
(V, ), de maneira universal, construtiva e como quantiza¸c˜ao da ´algebra exterior. Classificamos
todas as ´algebras de Clifford associadas as espa¸cos quadr´aticos de Minkowski
(Rp+q, p,q), onde p,q(u) = u21
+ ... + u2
p − (u2
p+1 + ... + u2
p+q), u = (u1, ..., up+q) ∈ Rp+q,
as quais denotamos por Clp,q, bem como suas complexifica¸c˜oes. Para tanto, usaremos
resultados importantes como o teorema da periodicidade de Carton/Bott. Al´em disso,
estudamos as suas representa¸c˜oes, destacando a Representa¸c˜ao Adjunta Torcida, as Representa
¸c˜oes Spin e Semi-Spin e por meio do n´umero de Radon-Hurwitz estudamos as
representa¸c˜oes das ´algebras Cl0,k.
| Identifer | oai:union.ndltd.org:IBICT/oai:tede.biblioteca.ufpb.br:tede/8039 |
| Date | 30 August 2013 |
| Creators | Farias, José Ginaldo de Sousa |
| Contributors | Tuesta, Napoleón Caro |
| Publisher | Universidade Federal da Paraíba, Programa de Pós-Graduação em Matemática, UFPB, Brasil, Matemática |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | Portuguese |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFPB, instname:Universidade Federal da Paraíba, instacron:UFPB |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 666657583566969084, 600, 600, 600, 600, -78633126427147401, -7090823417984401694, 2075167498588264571 |
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